id	sid	tid	token	lemma	pos
ejpam-5895	1	1	european	european	PROPN
ejpam-5895	1	2	journal	journal	PROPN
ejpam-5895	1	3	of	of	ADP
ejpam-5895	1	4	pure	pure	ADJ
ejpam-5895	1	5	and	and	CCONJ
ejpam-5895	1	6	applied	applied	ADJ
ejpam-5895	1	7	mathematics	mathematic	NOUN
ejpam-5895	1	8	2025	2025	NUM
ejpam-5895	1	9	,	,	PUNCT
ejpam-5895	1	10	vol	vol	NOUN
ejpam-5895	1	11	.	.	PROPN
ejpam-5895	1	12	18	18	NUM
ejpam-5895	1	13	,	,	PUNCT
ejpam-5895	1	14	issue	issue	NOUN
ejpam-5895	1	15	2	2	NUM
ejpam-5895	1	16	,	,	PUNCT
ejpam-5895	1	17	article	article	NOUN
ejpam-5895	1	18	number	number	NOUN
ejpam-5895	1	19	5895	5895	NUM
ejpam-5895	1	20	issn	issn	PROPN
ejpam-5895	1	21	1307	1307	NUM
ejpam-5895	1	22	-	-	SYM
ejpam-5895	1	23	5543	5543	NUM
ejpam-5895	1	24	–	–	PUNCT
ejpam-5895	1	25	ejpam.com	ejpam.com	X
ejpam-5895	1	26	published	publish	VERB
ejpam-5895	1	27	by	by	ADP
ejpam-5895	1	28	new	new	PROPN
ejpam-5895	1	29	york	york	PROPN
ejpam-5895	1	30	business	business	PROPN
ejpam-5895	1	31	global	global	PROPN
ejpam-5895	1	32	a	a	DET
ejpam-5895	1	33	comparative	comparative	ADJ
ejpam-5895	1	34	study	study	NOUN
ejpam-5895	1	35	of	of	ADP
ejpam-5895	1	36	finite	finite	ADJ
ejpam-5895	1	37	difference	difference	NOUN
ejpam-5895	1	38	and	and	CCONJ
ejpam-5895	1	39	galerkin	galerkin	PROPN
ejpam-5895	1	40	finite	finite	PROPN
ejpam-5895	1	41	element	element	NOUN
ejpam-5895	1	42	methods	method	NOUN
ejpam-5895	1	43	for	for	ADP
ejpam-5895	1	44	solving	solve	VERB
ejpam-5895	1	45	boundary	boundary	ADJ
ejpam-5895	1	46	value	value	NOUN
ejpam-5895	1	47	problems	problem	NOUN
ejpam-5895	1	48	shahad	shahad	VERB
ejpam-5895	1	49	saleh	saleh	PROPN
ejpam-5895	1	50	ayad	ayad	PROPN
ejpam-5895	1	51	almutairi1	almutairi1	PROPN
ejpam-5895	1	52	,	,	PUNCT
ejpam-5895	1	53	abdulkafi	abdulkafi	PROPN
ejpam-5895	1	54	mohammed	mohammed	PROPN
ejpam-5895	1	55	saeed1,∗	saeed1,∗	PROPN
ejpam-5895	1	56	1	1	NUM
ejpam-5895	1	57	department	department	NOUN
ejpam-5895	1	58	of	of	ADP
ejpam-5895	1	59	mathematics	mathematic	NOUN
ejpam-5895	1	60	,	,	PUNCT
ejpam-5895	1	61	college	college	NOUN
ejpam-5895	1	62	of	of	ADP
ejpam-5895	1	63	science	science	NOUN
ejpam-5895	1	64	,	,	PUNCT
ejpam-5895	1	65	qassim	qassim	PROPN
ejpam-5895	1	66	university	university	PROPN
ejpam-5895	1	67	,	,	PUNCT
ejpam-5895	1	68	buraydah	buraydah	NOUN
ejpam-5895	1	69	,	,	PUNCT
ejpam-5895	1	70	kingdom	kingdom	NOUN
ejpam-5895	1	71	of	of	ADP
ejpam-5895	1	72	saudi	saudi	PROPN
ejpam-5895	1	73	arabia	arabia	PROPN
ejpam-5895	1	74	abstract	abstract	NOUN
ejpam-5895	1	75	.	.	PUNCT
ejpam-5895	2	1	many	many	ADJ
ejpam-5895	2	2	applications	application	NOUN
ejpam-5895	2	3	in	in	ADP
ejpam-5895	2	4	engineering	engineering	NOUN
ejpam-5895	2	5	can	can	AUX
ejpam-5895	2	6	not	not	PART
ejpam-5895	2	7	be	be	AUX
ejpam-5895	2	8	solved	solve	VERB
ejpam-5895	2	9	analytically	analytically	ADV
ejpam-5895	2	10	,	,	PUNCT
ejpam-5895	2	11	major	major	ADJ
ejpam-5895	2	12	difficulty	difficulty	NOUN
ejpam-5895	2	13	in	in	ADP
ejpam-5895	2	14	the	the	DET
ejpam-5895	2	15	study	study	NOUN
ejpam-5895	2	16	of	of	ADP
ejpam-5895	2	17	partial	partial	ADJ
ejpam-5895	2	18	differential	differential	NOUN
ejpam-5895	2	19	equations	equation	NOUN
ejpam-5895	2	20	is	be	AUX
ejpam-5895	2	21	that	that	SCONJ
ejpam-5895	2	22	it	it	PRON
ejpam-5895	2	23	is	be	AUX
ejpam-5895	2	24	often	often	ADV
ejpam-5895	2	25	impossible	impossible	ADJ
ejpam-5895	2	26	to	to	PART
ejpam-5895	2	27	obtain	obtain	VERB
ejpam-5895	2	28	analytical	analytical	ADJ
ejpam-5895	2	29	solutions	solution	NOUN
ejpam-5895	2	30	.	.	PUNCT
ejpam-5895	3	1	therefore	therefore	ADV
ejpam-5895	3	2	,	,	PUNCT
ejpam-5895	3	3	various	various	ADJ
ejpam-5895	3	4	numerical	numerical	ADJ
ejpam-5895	3	5	methods	method	NOUN
ejpam-5895	3	6	for	for	ADP
ejpam-5895	3	7	solving	solve	VERB
ejpam-5895	3	8	partial	partial	ADJ
ejpam-5895	3	9	differential	differential	NOUN
ejpam-5895	3	10	equations	equation	NOUN
ejpam-5895	3	11	have	have	AUX
ejpam-5895	3	12	been	be	AUX
ejpam-5895	3	13	proposed	propose	VERB
ejpam-5895	3	14	by	by	ADP
ejpam-5895	3	15	related	related	ADJ
ejpam-5895	3	16	researchers	researcher	NOUN
ejpam-5895	3	17	,	,	PUNCT
ejpam-5895	3	18	such	such	ADJ
ejpam-5895	3	19	as	as	ADP
ejpam-5895	3	20	the	the	DET
ejpam-5895	3	21	finite	finite	ADJ
ejpam-5895	3	22	difference	difference	NOUN
ejpam-5895	3	23	method	method	NOUN
ejpam-5895	3	24	(	(	PUNCT
ejpam-5895	3	25	fdm	fdm	NOUN
ejpam-5895	3	26	)	)	PUNCT
ejpam-5895	3	27	,	,	PUNCT
ejpam-5895	3	28	finite	finite	PROPN
ejpam-5895	3	29	element	element	NOUN
ejpam-5895	3	30	method	method	NOUN
ejpam-5895	3	31	(	(	PUNCT
ejpam-5895	3	32	fem	fem	PROPN
ejpam-5895	3	33	)	)	PUNCT
ejpam-5895	3	34	,	,	PUNCT
ejpam-5895	3	35	finite	finite	ADJ
ejpam-5895	3	36	volume	volume	NOUN
ejpam-5895	3	37	method	method	NOUN
ejpam-5895	3	38	(	(	PUNCT
ejpam-5895	3	39	fvm	fvm	ADV
ejpam-5895	3	40	)	)	PUNCT
ejpam-5895	3	41	,	,	PUNCT
ejpam-5895	3	42	etc	etc	X
ejpam-5895	3	43	.	.	X
ejpam-5895	4	1	the	the	DET
ejpam-5895	4	2	earliest	early	ADJ
ejpam-5895	4	3	is	be	AUX
ejpam-5895	4	4	the	the	DET
ejpam-5895	4	5	fdm	fdm	NOUN
ejpam-5895	4	6	,	,	PUNCT
ejpam-5895	4	7	which	which	PRON
ejpam-5895	4	8	approximates	approximate	VERB
ejpam-5895	4	9	the	the	DET
ejpam-5895	4	10	differential	differential	ADJ
ejpam-5895	4	11	equations	equation	NOUN
ejpam-5895	4	12	by	by	ADP
ejpam-5895	4	13	using	use	VERB
ejpam-5895	4	14	a	a	DET
ejpam-5895	4	15	local	local	ADJ
ejpam-5895	4	16	taylor	taylor	NOUN
ejpam-5895	4	17	expansion	expansion	NOUN
ejpam-5895	4	18	.	.	PUNCT
ejpam-5895	5	1	the	the	DET
ejpam-5895	5	2	finite	finite	PROPN
ejpam-5895	5	3	element	element	NOUN
ejpam-5895	5	4	method	method	NOUN
ejpam-5895	5	5	(	(	PUNCT
ejpam-5895	5	6	fem	fem	NOUN
ejpam-5895	5	7	)	)	PUNCT
ejpam-5895	5	8	is	be	AUX
ejpam-5895	5	9	a	a	DET
ejpam-5895	5	10	numerical	numerical	ADJ
ejpam-5895	5	11	technique	technique	NOUN
ejpam-5895	5	12	for	for	ADP
ejpam-5895	5	13	solving	solve	VERB
ejpam-5895	5	14	problems	problem	NOUN
ejpam-5895	5	15	which	which	PRON
ejpam-5895	5	16	are	be	AUX
ejpam-5895	5	17	described	describe	VERB
ejpam-5895	5	18	by	by	ADP
ejpam-5895	5	19	partial	partial	ADJ
ejpam-5895	5	20	differential	differential	ADJ
ejpam-5895	5	21	equations	equation	NOUN
ejpam-5895	5	22	or	or	CCONJ
ejpam-5895	5	23	can	can	AUX
ejpam-5895	5	24	be	be	AUX
ejpam-5895	5	25	formulated	formulate	VERB
ejpam-5895	5	26	as	as	ADP
ejpam-5895	5	27	functional	functional	ADJ
ejpam-5895	5	28	minimization	minimization	NOUN
ejpam-5895	5	29	.	.	PUNCT
ejpam-5895	6	1	a	a	DET
ejpam-5895	6	2	domain	domain	NOUN
ejpam-5895	6	3	of	of	ADP
ejpam-5895	6	4	interest	interest	NOUN
ejpam-5895	6	5	is	be	AUX
ejpam-5895	6	6	represented	represent	VERB
ejpam-5895	6	7	as	as	ADP
ejpam-5895	6	8	an	an	DET
ejpam-5895	6	9	assembly	assembly	NOUN
ejpam-5895	6	10	of	of	ADP
ejpam-5895	6	11	finite	finite	ADJ
ejpam-5895	6	12	elements.this	elements.this	PRON
ejpam-5895	6	13	paper	paper	NOUN
ejpam-5895	6	14	presents	present	VERB
ejpam-5895	6	15	a	a	DET
ejpam-5895	6	16	qualitative	qualitative	ADJ
ejpam-5895	6	17	comparative	comparative	ADJ
ejpam-5895	6	18	study	study	NOUN
ejpam-5895	6	19	of	of	ADP
ejpam-5895	6	20	fdm	fdm	NOUN
ejpam-5895	6	21	and	and	CCONJ
ejpam-5895	6	22	galerkin	galerkin	PROPN
ejpam-5895	6	23	finite	finite	PROPN
ejpam-5895	6	24	element	element	NOUN
ejpam-5895	6	25	method	method	NOUN
ejpam-5895	6	26	(	(	PUNCT
ejpam-5895	6	27	gfem	gfem	PROPN
ejpam-5895	6	28	)	)	PUNCT
ejpam-5895	6	29	to	to	PART
ejpam-5895	6	30	show	show	VERB
ejpam-5895	6	31	the	the	DET
ejpam-5895	6	32	advantages	advantage	NOUN
ejpam-5895	6	33	and	and	CCONJ
ejpam-5895	6	34	disadvantages	disadvantage	NOUN
ejpam-5895	6	35	of	of	ADP
ejpam-5895	6	36	these	these	DET
ejpam-5895	6	37	methods	method	NOUN
ejpam-5895	6	38	in	in	ADP
ejpam-5895	6	39	solving	solve	VERB
ejpam-5895	6	40	boundary	boundary	ADJ
ejpam-5895	6	41	value	value	NOUN
ejpam-5895	6	42	problems	problem	NOUN
ejpam-5895	6	43	.	.	PUNCT
ejpam-5895	7	1	several	several	ADJ
ejpam-5895	7	2	numerical	numerical	ADJ
ejpam-5895	7	3	experiments	experiment	NOUN
ejpam-5895	7	4	conducted	conduct	VERB
ejpam-5895	7	5	for	for	ADP
ejpam-5895	7	6	comparisons	comparison	NOUN
ejpam-5895	7	7	purpose	purpose	NOUN
ejpam-5895	7	8	.	.	PUNCT
ejpam-5895	8	1	the	the	DET
ejpam-5895	8	2	results	result	NOUN
ejpam-5895	8	3	reveal	reveal	VERB
ejpam-5895	8	4	that	that	SCONJ
ejpam-5895	8	5	the	the	DET
ejpam-5895	8	6	gfem	gfem	NOUN
ejpam-5895	8	7	is	be	AUX
ejpam-5895	8	8	an	an	DET
ejpam-5895	8	9	alternative	alternative	ADJ
ejpam-5895	8	10	method	method	NOUN
ejpam-5895	8	11	for	for	ADP
ejpam-5895	8	12	solving	solve	VERB
ejpam-5895	8	13	several	several	ADJ
ejpam-5895	8	14	types	type	NOUN
ejpam-5895	8	15	of	of	ADP
ejpam-5895	8	16	boundary	boundary	ADJ
ejpam-5895	8	17	value	value	NOUN
ejpam-5895	8	18	problems	problem	NOUN
ejpam-5895	8	19	.	.	PUNCT
ejpam-5895	9	1	2020	2020	NUM
ejpam-5895	9	2	mathematics	mathematic	NOUN
ejpam-5895	9	3	subject	subject	NOUN
ejpam-5895	9	4	classifications	classification	NOUN
ejpam-5895	9	5	:	:	PUNCT
ejpam-5895	9	6	76s05	76s05	NUM
ejpam-5895	9	7	,	,	PUNCT
ejpam-5895	9	8	76d10	76d10	NUM
ejpam-5895	9	9	,	,	PUNCT
ejpam-5895	9	10	80a32	80a32	NUM
ejpam-5895	9	11	,	,	PUNCT
ejpam-5895	9	12	35q79	35q79	NUM
ejpam-5895	9	13	key	key	ADJ
ejpam-5895	9	14	words	word	NOUN
ejpam-5895	9	15	and	and	CCONJ
ejpam-5895	9	16	phrases	phrase	NOUN
ejpam-5895	9	17	:	:	PUNCT
ejpam-5895	9	18	boundary	boundary	ADJ
ejpam-5895	9	19	value	value	NOUN
ejpam-5895	9	20	problem	problem	NOUN
ejpam-5895	9	21	,	,	PUNCT
ejpam-5895	9	22	finite	finite	ADJ
ejpam-5895	9	23	difference	difference	NOUN
ejpam-5895	9	24	method	method	NOUN
ejpam-5895	9	25	,	,	PUNCT
ejpam-5895	9	26	galerkin	galerkin	PROPN
ejpam-5895	9	27	finite	finite	PROPN
ejpam-5895	9	28	element	element	PROPN
ejpam-5895	9	29	method	method	NOUN
ejpam-5895	9	30	,	,	PUNCT
ejpam-5895	9	31	poisson	poisson	PROPN
ejpam-5895	9	32	’s	’s	PART
ejpam-5895	9	33	equation	equation	NOUN
ejpam-5895	9	34	1	1	NUM
ejpam-5895	9	35	.	.	PUNCT
ejpam-5895	10	1	introduction	introduction	NOUN
ejpam-5895	10	2	there	there	PRON
ejpam-5895	10	3	are	be	VERB
ejpam-5895	10	4	several	several	ADJ
ejpam-5895	10	5	applications	application	NOUN
ejpam-5895	10	6	of	of	ADP
ejpam-5895	10	7	poisson	poisson	NOUN
ejpam-5895	10	8	’s	’s	PART
ejpam-5895	10	9	equation	equation	NOUN
ejpam-5895	10	10	in	in	ADP
ejpam-5895	10	11	both	both	DET
ejpam-5895	10	12	engineering	engineering	NOUN
ejpam-5895	10	13	and	and	CCONJ
ejpam-5895	10	14	physics	physics	NOUN
ejpam-5895	10	15	.	.	PUNCT
ejpam-5895	11	1	it	it	PRON
ejpam-5895	11	2	is	be	AUX
ejpam-5895	11	3	employed	employ	VERB
ejpam-5895	11	4	to	to	PART
ejpam-5895	11	5	resolve	resolve	VERB
ejpam-5895	11	6	issues	issue	NOUN
ejpam-5895	11	7	in	in	ADP
ejpam-5895	11	8	fluid	fluid	ADJ
ejpam-5895	11	9	dynamics	dynamic	NOUN
ejpam-5895	11	10	,	,	PUNCT
ejpam-5895	11	11	quantum	quantum	NOUN
ejpam-5895	11	12	mechanics	mechanic	NOUN
ejpam-5895	11	13	,	,	PUNCT
ejpam-5895	11	14	electrostatics	electrostatic	NOUN
ejpam-5895	11	15	,	,	PUNCT
ejpam-5895	11	16	and	and	CCONJ
ejpam-5895	11	17	magnetostatics	magnetostatic	NOUN
ejpam-5895	11	18	.	.	PUNCT
ejpam-5895	12	1	poisson	poisson	PROPN
ejpam-5895	12	2	’s	’s	PART
ejpam-5895	12	3	equation	equation	NOUN
ejpam-5895	12	4	connects	connect	VERB
ejpam-5895	12	5	the	the	DET
ejpam-5895	12	6	electric	electric	ADJ
ejpam-5895	12	7	potential	potential	NOUN
ejpam-5895	12	8	to	to	ADP
ejpam-5895	12	9	the	the	DET
ejpam-5895	12	10	charge	charge	NOUN
ejpam-5895	12	11	distribution	distribution	NOUN
ejpam-5895	12	12	in	in	ADP
ejpam-5895	12	13	electrostatics	electrostatic	NOUN
ejpam-5895	12	14	.	.	PUNCT
ejpam-5895	13	1	it	it	PRON
ejpam-5895	13	2	connects	connect	VERB
ejpam-5895	13	3	the	the	DET
ejpam-5895	13	4	magnetic	magnetic	ADJ
ejpam-5895	13	5	potential	potential	NOUN
ejpam-5895	13	6	to	to	ADP
ejpam-5895	13	7	the	the	DET
ejpam-5895	13	8	current	current	ADJ
ejpam-5895	13	9	distribution	distribution	NOUN
ejpam-5895	13	10	in	in	ADP
ejpam-5895	13	11	magnetostatics	magnetostatic	NOUN
ejpam-5895	13	12	.	.	PUNCT
ejpam-5895	14	1	for	for	ADP
ejpam-5895	14	2	scientists	scientist	NOUN
ejpam-5895	14	3	and	and	CCONJ
ejpam-5895	14	4	engineers	engineer	NOUN
ejpam-5895	14	5	investigating	investigate	VERB
ejpam-5895	14	6	the	the	DET
ejpam-5895	14	7	behavior	behavior	NOUN
ejpam-5895	14	8	of	of	ADP
ejpam-5895	14	9	physical	physical	ADJ
ejpam-5895	14	10	systems	system	NOUN
ejpam-5895	14	11	,	,	PUNCT
ejpam-5895	14	12	the	the	DET
ejpam-5895	14	13	equation	equation	NOUN
ejpam-5895	14	14	is	be	AUX
ejpam-5895	14	15	a	a	DET
ejpam-5895	14	16	crucial	crucial	ADJ
ejpam-5895	14	17	tool	tool	NOUN
ejpam-5895	14	18	[	[	X
ejpam-5895	14	19	1–3	1–3	NOUN
ejpam-5895	14	20	]	]	X
ejpam-5895	14	21	.	.	PUNCT
ejpam-5895	15	1	∗corresponding	∗corresponde	VERB
ejpam-5895	15	2	author	author	NOUN
ejpam-5895	15	3	.	.	PUNCT
ejpam-5895	16	1	doi	doi	NOUN
ejpam-5895	16	2	:	:	PUNCT
ejpam-5895	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5895	https://doi.org/10.29020/nybg.ejpam.v18i2.5895	PROPN
ejpam-5895	16	4	email	email	NOUN
ejpam-5895	16	5	address	address	NOUN
ejpam-5895	16	6	:	:	PUNCT
ejpam-5895	16	7	441212396@qu.edu.sa	441212396@qu.edu.sa	PROPN
ejpam-5895	16	8	(	(	PUNCT
ejpam-5895	16	9	s.	s.	PROPN
ejpam-5895	16	10	s.	s.	PROPN
ejpam-5895	16	11	almutairi	almutairi	PROPN
ejpam-5895	16	12	)	)	PUNCT
ejpam-5895	16	13	,	,	PUNCT
ejpam-5895	16	14	abdulkafi.ahmed@qu.edu.sa	abdulkafi.ahmed@qu.edu.sa	PROPN
ejpam-5895	16	15	(	(	PUNCT
ejpam-5895	16	16	a.	a.	PROPN
ejpam-5895	16	17	m.	m.	PROPN
ejpam-5895	16	18	saeed	saeed	PROPN
ejpam-5895	16	19	)	)	PUNCT
ejpam-5895	16	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5895	17	1	1	1	NUM
ejpam-5895	17	2	copyright	copyright	NOUN
ejpam-5895	17	3	:	:	PUNCT
ejpam-5895	17	4	©	©	PROPN
ejpam-5895	17	5	2025	2025	NUM
ejpam-5895	17	6	the	the	DET
ejpam-5895	17	7	author(s	author(s	NOUN
ejpam-5895	17	8	)	)	PUNCT
ejpam-5895	17	9	.	.	PUNCT
ejpam-5895	18	1	(	(	PUNCT
ejpam-5895	18	2	cc	cc	NOUN
ejpam-5895	18	3	by	by	ADP
ejpam-5895	18	4	-	-	PUNCT
ejpam-5895	18	5	nc	nc	PROPN
ejpam-5895	18	6	4.0	4.0	NUM
ejpam-5895	18	7	)	)	PUNCT
ejpam-5895	18	8	s.	s.	PROPN
ejpam-5895	18	9	s.	s.	PROPN
ejpam-5895	18	10	almutairi	almutairi	PROPN
ejpam-5895	18	11	,	,	PUNCT
ejpam-5895	18	12	a.	a.	PROPN
ejpam-5895	18	13	m.	m.	PROPN
ejpam-5895	18	14	saeed	saeed	PROPN
ejpam-5895	18	15	/	/	SYM
ejpam-5895	18	16	eur	eur	PROPN
ejpam-5895	18	17	.	.	PUNCT
ejpam-5895	19	1	j.	j.	PROPN
ejpam-5895	19	2	pure	pure	PROPN
ejpam-5895	19	3	appl	appl	PROPN
ejpam-5895	19	4	.	.	PROPN
ejpam-5895	19	5	math	math	PROPN
ejpam-5895	19	6	,	,	PUNCT
ejpam-5895	19	7	18	18	NUM
ejpam-5895	19	8	(	(	PUNCT
ejpam-5895	19	9	2	2	NUM
ejpam-5895	19	10	)	)	PUNCT
ejpam-5895	19	11	(	(	PUNCT
ejpam-5895	19	12	2025	2025	NUM
ejpam-5895	19	13	)	)	PUNCT
ejpam-5895	19	14	,	,	PUNCT
ejpam-5895	19	15	5895	5895	NUM
ejpam-5895	19	16	2	2	NUM
ejpam-5895	19	17	of	of	ADP
ejpam-5895	19	18	10	10	NUM
ejpam-5895	19	19	the	the	DET
ejpam-5895	19	20	complexity	complexity	NOUN
ejpam-5895	19	21	of	of	ADP
ejpam-5895	19	22	many	many	ADJ
ejpam-5895	19	23	differential	differential	ADJ
ejpam-5895	19	24	equations	equation	NOUN
ejpam-5895	19	25	that	that	PRON
ejpam-5895	19	26	arise	arise	VERB
ejpam-5895	19	27	in	in	ADP
ejpam-5895	19	28	applications	application	NOUN
ejpam-5895	19	29	makes	make	VERB
ejpam-5895	19	30	it	it	PRON
ejpam-5895	19	31	occasionally	occasionally	ADV
ejpam-5895	19	32	impracticable	impracticable	ADJ
ejpam-5895	19	33	to	to	PART
ejpam-5895	19	34	have	have	VERB
ejpam-5895	19	35	solution	solution	NOUN
ejpam-5895	19	36	formulae	formulae	ADJ
ejpam-5895	19	37	;	;	PUNCT
ejpam-5895	19	38	if	if	SCONJ
ejpam-5895	19	39	one	one	PRON
ejpam-5895	19	40	is	be	AUX
ejpam-5895	19	41	available	available	ADJ
ejpam-5895	19	42	,	,	PUNCT
ejpam-5895	19	43	it	it	PRON
ejpam-5895	19	44	may	may	AUX
ejpam-5895	19	45	include	include	VERB
ejpam-5895	19	46	integrals	integral	NOUN
ejpam-5895	19	47	that	that	PRON
ejpam-5895	19	48	can	can	AUX
ejpam-5895	19	49	only	only	ADV
ejpam-5895	19	50	be	be	AUX
ejpam-5895	19	51	computed	compute	VERB
ejpam-5895	19	52	via	via	ADP
ejpam-5895	19	53	a	a	DET
ejpam-5895	19	54	numerical	numerical	ADJ
ejpam-5895	19	55	quadrature	quadrature	NOUN
ejpam-5895	19	56	formula	formula	NOUN
ejpam-5895	19	57	.	.	PUNCT
ejpam-5895	20	1	numerical	numerical	ADJ
ejpam-5895	20	2	techniques	technique	NOUN
ejpam-5895	20	3	offer	offer	VERB
ejpam-5895	20	4	a	a	DET
ejpam-5895	20	5	potent	potent	ADJ
ejpam-5895	20	6	substitute	substitute	NOUN
ejpam-5895	20	7	tool	tool	NOUN
ejpam-5895	20	8	for	for	ADP
ejpam-5895	20	9	resolving	resolve	VERB
ejpam-5895	20	10	differential	differential	ADJ
ejpam-5895	20	11	equations	equation	NOUN
ejpam-5895	20	12	under	under	ADP
ejpam-5895	20	13	the	the	DET
ejpam-5895	20	14	specified	specified	ADJ
ejpam-5895	20	15	initial	initial	ADJ
ejpam-5895	20	16	condition	condition	NOUN
ejpam-5895	20	17	or	or	CCONJ
ejpam-5895	20	18	conditions	condition	NOUN
ejpam-5895	20	19	in	in	ADP
ejpam-5895	20	20	either	either	DET
ejpam-5895	20	21	scenario	scenario	NOUN
ejpam-5895	20	22	.	.	PUNCT
ejpam-5895	21	1	the	the	DET
ejpam-5895	21	2	finite	finite	ADJ
ejpam-5895	21	3	difference	difference	NOUN
ejpam-5895	21	4	method	method	NOUN
ejpam-5895	21	5	(	(	PUNCT
ejpam-5895	21	6	fdm	fdm	NOUN
ejpam-5895	21	7	)	)	PUNCT
ejpam-5895	21	8	,	,	PUNCT
ejpam-5895	21	9	finite	finite	PROPN
ejpam-5895	21	10	element	element	NOUN
ejpam-5895	21	11	method	method	NOUN
ejpam-5895	21	12	(	(	PUNCT
ejpam-5895	21	13	fem	fem	NOUN
ejpam-5895	21	14	)	)	PUNCT
ejpam-5895	21	15	,	,	PUNCT
ejpam-5895	21	16	and	and	CCONJ
ejpam-5895	21	17	finite	finite	ADJ
ejpam-5895	21	18	volume	volume	NOUN
ejpam-5895	21	19	method	method	NOUN
ejpam-5895	21	20	(	(	PUNCT
ejpam-5895	21	21	fvm	fvm	ADV
ejpam-5895	21	22	)	)	PUNCT
ejpam-5895	21	23	are	be	AUX
ejpam-5895	21	24	the	the	DET
ejpam-5895	21	25	three	three	NUM
ejpam-5895	21	26	traditional	traditional	ADJ
ejpam-5895	21	27	options	option	NOUN
ejpam-5895	21	28	for	for	ADP
ejpam-5895	21	29	numerically	numerically	ADV
ejpam-5895	21	30	solving	solve	VERB
ejpam-5895	21	31	pdes	pde	NOUN
ejpam-5895	21	32	.	.	PUNCT
ejpam-5895	22	1	the	the	DET
ejpam-5895	22	2	earliest	early	ADJ
ejpam-5895	22	3	is	be	AUX
ejpam-5895	22	4	the	the	DET
ejpam-5895	22	5	fdm	fdm	NOUN
ejpam-5895	22	6	,	,	PUNCT
ejpam-5895	22	7	which	which	PRON
ejpam-5895	22	8	approximates	approximate	VERB
ejpam-5895	22	9	the	the	DET
ejpam-5895	22	10	differential	differential	ADJ
ejpam-5895	22	11	equations	equation	NOUN
ejpam-5895	22	12	by	by	ADP
ejpam-5895	22	13	using	use	VERB
ejpam-5895	22	14	a	a	DET
ejpam-5895	22	15	local	local	ADJ
ejpam-5895	22	16	taylor	taylor	NOUN
ejpam-5895	22	17	expansion	expansion	NOUN
ejpam-5895	23	1	[	[	X
ejpam-5895	23	2	1	1	NUM
ejpam-5895	23	3	,	,	PUNCT
ejpam-5895	23	4	2	2	NUM
ejpam-5895	23	5	]	]	PUNCT
ejpam-5895	23	6	.	.	PUNCT
ejpam-5895	24	1	the	the	DET
ejpam-5895	24	2	discretization	discretization	NOUN
ejpam-5895	24	3	of	of	ADP
ejpam-5895	24	4	the	the	DET
ejpam-5895	24	5	pde	pde	NOUN
ejpam-5895	24	6	is	be	AUX
ejpam-5895	24	7	constructed	construct	VERB
ejpam-5895	24	8	by	by	ADP
ejpam-5895	24	9	the	the	DET
ejpam-5895	24	10	fdm	fdm	NOUN
ejpam-5895	24	11	using	use	VERB
ejpam-5895	24	12	a	a	DET
ejpam-5895	24	13	topologically	topologically	ADV
ejpam-5895	24	14	square	square	ADJ
ejpam-5895	24	15	network	network	NOUN
ejpam-5895	24	16	of	of	ADP
ejpam-5895	24	17	lines	line	NOUN
ejpam-5895	24	18	.	.	PUNCT
ejpam-5895	25	1	this	this	PRON
ejpam-5895	25	2	might	might	AUX
ejpam-5895	25	3	be	be	AUX
ejpam-5895	25	4	a	a	DET
ejpam-5895	25	5	method	method	NOUN
ejpam-5895	25	6	’s	’s	PART
ejpam-5895	25	7	bottleneck	bottleneck	NOUN
ejpam-5895	25	8	when	when	SCONJ
ejpam-5895	25	9	working	work	VERB
ejpam-5895	25	10	with	with	ADP
ejpam-5895	25	11	intricate	intricate	ADJ
ejpam-5895	25	12	geometries	geometry	NOUN
ejpam-5895	25	13	in	in	ADP
ejpam-5895	25	14	several	several	ADJ
ejpam-5895	25	15	dimensions	dimension	NOUN
ejpam-5895	25	16	.	.	PUNCT
ejpam-5895	26	1	this	this	DET
ejpam-5895	26	2	difficulty	difficulty	NOUN
ejpam-5895	26	3	encouraged	encourage	VERB
ejpam-5895	26	4	the	the	DET
ejpam-5895	26	5	adoption	adoption	NOUN
ejpam-5895	26	6	of	of	ADP
ejpam-5895	26	7	an	an	DET
ejpam-5895	26	8	integral	integral	ADJ
ejpam-5895	26	9	form	form	NOUN
ejpam-5895	26	10	of	of	ADP
ejpam-5895	26	11	the	the	DET
ejpam-5895	26	12	pdes	pde	NOUN
ejpam-5895	26	13	,	,	PUNCT
ejpam-5895	26	14	followed	follow	VERB
ejpam-5895	26	15	by	by	ADP
ejpam-5895	26	16	the	the	DET
ejpam-5895	26	17	development	development	NOUN
ejpam-5895	26	18	of	of	ADP
ejpam-5895	26	19	the	the	DET
ejpam-5895	26	20	finite	finite	ADJ
ejpam-5895	26	21	element	element	NOUN
ejpam-5895	26	22	and	and	CCONJ
ejpam-5895	26	23	finite	finite	ADJ
ejpam-5895	26	24	volume	volume	NOUN
ejpam-5895	26	25	approaches	approach	VERB
ejpam-5895	27	1	[	[	X
ejpam-5895	27	2	3–5	3–5	NOUN
ejpam-5895	27	3	]	]	PUNCT
ejpam-5895	27	4	.	.	PUNCT
ejpam-5895	28	1	discretization	discretization	NOUN
ejpam-5895	28	2	to	to	PART
ejpam-5895	28	3	approximate	approximate	ADJ
ejpam-5895	28	4	differential	differential	ADJ
ejpam-5895	28	5	equation	equation	NOUN
ejpam-5895	28	6	solutions	solution	NOUN
ejpam-5895	28	7	.	.	PUNCT
ejpam-5895	29	1	this	this	DET
ejpam-5895	29	2	method	method	NOUN
ejpam-5895	29	3	converts	convert	VERB
ejpam-5895	29	4	continuous	continuous	ADJ
ejpam-5895	29	5	functions	function	NOUN
ejpam-5895	29	6	into	into	ADP
ejpam-5895	29	7	discrete	discrete	ADJ
ejpam-5895	29	8	ones	one	NOUN
ejpam-5895	29	9	,	,	PUNCT
ejpam-5895	29	10	simplifying	simplify	VERB
ejpam-5895	29	11	calculation	calculation	NOUN
ejpam-5895	29	12	and	and	CCONJ
ejpam-5895	29	13	analysis	analysis	NOUN
ejpam-5895	29	14	.	.	PUNCT
ejpam-5895	30	1	it	it	PRON
ejpam-5895	30	2	is	be	AUX
ejpam-5895	30	3	commonly	commonly	ADV
ejpam-5895	30	4	used	use	VERB
ejpam-5895	30	5	in	in	ADP
ejpam-5895	30	6	domains	domain	NOUN
ejpam-5895	30	7	with	with	ADP
ejpam-5895	30	8	differential	differential	ADJ
ejpam-5895	30	9	equations	equation	NOUN
ejpam-5895	30	10	,	,	PUNCT
ejpam-5895	30	11	including	include	VERB
ejpam-5895	30	12	physics	physics	NOUN
ejpam-5895	30	13	,	,	PUNCT
ejpam-5895	30	14	engineering	engineering	NOUN
ejpam-5895	30	15	,	,	PUNCT
ejpam-5895	30	16	and	and	CCONJ
ejpam-5895	30	17	finance	finance	NOUN
ejpam-5895	30	18	.	.	PUNCT
ejpam-5895	31	1	there	there	PRON
ejpam-5895	31	2	are	be	VERB
ejpam-5895	31	3	three	three	NUM
ejpam-5895	31	4	forms	form	NOUN
ejpam-5895	31	5	of	of	ADP
ejpam-5895	31	6	finite	finite	ADJ
ejpam-5895	31	7	difference	difference	NOUN
ejpam-5895	31	8	approximations	approximation	NOUN
ejpam-5895	31	9	:	:	PUNCT
ejpam-5895	31	10	forward	forward	ADJ
ejpam-5895	31	11	difference	difference	NOUN
ejpam-5895	31	12	,	,	PUNCT
ejpam-5895	31	13	backward	backward	ADJ
ejpam-5895	31	14	difference	difference	NOUN
ejpam-5895	31	15	,	,	PUNCT
ejpam-5895	31	16	and	and	CCONJ
ejpam-5895	31	17	central	central	ADJ
ejpam-5895	31	18	difference	difference	NOUN
ejpam-5895	31	19	.	.	PUNCT
ejpam-5895	32	1	the	the	DET
ejpam-5895	32	2	forward	forward	ADJ
ejpam-5895	32	3	difference	difference	NOUN
ejpam-5895	32	4	method	method	NOUN
ejpam-5895	32	5	estimates	estimate	VERB
ejpam-5895	32	6	the	the	DET
ejpam-5895	32	7	derivative	derivative	NOUN
ejpam-5895	32	8	by	by	ADP
ejpam-5895	32	9	comparing	compare	VERB
ejpam-5895	32	10	the	the	DET
ejpam-5895	32	11	value	value	NOUN
ejpam-5895	32	12	of	of	ADP
ejpam-5895	32	13	the	the	DET
ejpam-5895	32	14	function	function	NOUN
ejpam-5895	32	15	at	at	ADP
ejpam-5895	32	16	one	one	NUM
ejpam-5895	32	17	point	point	NOUN
ejpam-5895	32	18	to	to	ADP
ejpam-5895	32	19	the	the	DET
ejpam-5895	32	20	next	next	ADJ
ejpam-5895	32	21	.	.	PUNCT
ejpam-5895	33	1	the	the	DET
ejpam-5895	33	2	backward	backward	ADJ
ejpam-5895	33	3	difference	difference	NOUN
ejpam-5895	33	4	compares	compare	VERB
ejpam-5895	33	5	the	the	DET
ejpam-5895	33	6	values	value	NOUN
ejpam-5895	33	7	at	at	ADP
ejpam-5895	33	8	the	the	DET
ejpam-5895	33	9	present	present	ADJ
ejpam-5895	33	10	and	and	CCONJ
ejpam-5895	33	11	prior	prior	ADJ
ejpam-5895	33	12	points	point	NOUN
ejpam-5895	33	13	.	.	PUNCT
ejpam-5895	34	1	the	the	DET
ejpam-5895	34	2	central	central	ADJ
ejpam-5895	34	3	difference	difference	NOUN
ejpam-5895	34	4	is	be	AUX
ejpam-5895	34	5	a	a	DET
ejpam-5895	34	6	more	more	ADV
ejpam-5895	34	7	accurate	accurate	ADJ
ejpam-5895	34	8	estimate	estimate	NOUN
ejpam-5895	34	9	since	since	SCONJ
ejpam-5895	34	10	it	it	PRON
ejpam-5895	34	11	averages	average	VERB
ejpam-5895	34	12	the	the	DET
ejpam-5895	34	13	forward	forward	ADJ
ejpam-5895	34	14	and	and	CCONJ
ejpam-5895	34	15	backward	backward	ADJ
ejpam-5895	34	16	differences	difference	NOUN
ejpam-5895	34	17	.	.	PUNCT
ejpam-5895	35	1	among	among	ADP
ejpam-5895	35	2	the	the	DET
ejpam-5895	35	3	numerical	numerical	ADJ
ejpam-5895	35	4	techniques	technique	NOUN
ejpam-5895	35	5	developed	develop	VERB
ejpam-5895	35	6	over	over	ADP
ejpam-5895	35	7	many	many	ADJ
ejpam-5895	35	8	decades	decade	NOUN
ejpam-5895	35	9	is	be	AUX
ejpam-5895	35	10	the	the	DET
ejpam-5895	35	11	fdm	fdm	NOUN
ejpam-5895	35	12	.	.	PUNCT
ejpam-5895	36	1	the	the	DET
ejpam-5895	36	2	technique	technique	NOUN
ejpam-5895	36	3	can	can	AUX
ejpam-5895	36	4	be	be	AUX
ejpam-5895	36	5	used	use	VERB
ejpam-5895	36	6	to	to	PART
ejpam-5895	36	7	solve	solve	VERB
ejpam-5895	36	8	partial	partial	ADJ
ejpam-5895	36	9	differential	differential	NOUN
ejpam-5895	36	10	equations	equation	NOUN
ejpam-5895	36	11	by	by	ADP
ejpam-5895	36	12	approximating	approximate	VERB
ejpam-5895	36	13	them	they	PRON
ejpam-5895	36	14	with	with	ADP
ejpam-5895	36	15	the	the	DET
ejpam-5895	36	16	taylor	taylor	PROPN
ejpam-5895	36	17	series	series	NOUN
ejpam-5895	36	18	[	[	X
ejpam-5895	36	19	6	6	NUM
ejpam-5895	36	20	,	,	PUNCT
ejpam-5895	36	21	7	7	NUM
ejpam-5895	36	22	]	]	PUNCT
ejpam-5895	36	23	.	.	PUNCT
ejpam-5895	37	1	on	on	ADP
ejpam-5895	37	2	the	the	DET
ejpam-5895	37	3	other	other	ADJ
ejpam-5895	37	4	hand	hand	NOUN
ejpam-5895	37	5	,	,	PUNCT
ejpam-5895	37	6	the	the	DET
ejpam-5895	37	7	fem	fem	NOUN
ejpam-5895	37	8	is	be	AUX
ejpam-5895	37	9	a	a	DET
ejpam-5895	37	10	numerical	numerical	ADJ
ejpam-5895	37	11	technique	technique	NOUN
ejpam-5895	37	12	typically	typically	ADV
ejpam-5895	37	13	employed	employ	VERB
ejpam-5895	37	14	to	to	PART
ejpam-5895	37	15	resolve	resolve	VERB
ejpam-5895	37	16	differential	differential	ADJ
ejpam-5895	37	17	equations	equation	NOUN
ejpam-5895	37	18	containing	contain	VERB
ejpam-5895	37	19	boundary	boundary	ADJ
ejpam-5895	37	20	conditions	condition	NOUN
ejpam-5895	37	21	.	.	PUNCT
ejpam-5895	38	1	using	use	VERB
ejpam-5895	38	2	a	a	DET
ejpam-5895	38	3	sufficient	sufficient	ADJ
ejpam-5895	38	4	set	set	NOUN
ejpam-5895	38	5	of	of	ADP
ejpam-5895	38	6	basis	basis	NOUN
ejpam-5895	38	7	functions	function	NOUN
ejpam-5895	38	8	,	,	PUNCT
ejpam-5895	38	9	the	the	DET
ejpam-5895	38	10	fem	fem	NOUN
ejpam-5895	38	11	approximates	approximate	VERB
ejpam-5895	38	12	the	the	DET
ejpam-5895	38	13	solution	solution	NOUN
ejpam-5895	38	14	of	of	ADP
ejpam-5895	38	15	the	the	DET
ejpam-5895	38	16	differential	differential	ADJ
ejpam-5895	38	17	equation	equation	NOUN
ejpam-5895	38	18	on	on	ADP
ejpam-5895	38	19	the	the	DET
ejpam-5895	38	20	domain	domain	NOUN
ejpam-5895	38	21	by	by	ADP
ejpam-5895	38	22	dividing	divide	VERB
ejpam-5895	38	23	it	it	PRON
ejpam-5895	38	24	into	into	ADP
ejpam-5895	38	25	a	a	DET
ejpam-5895	38	26	finite	finite	ADJ
ejpam-5895	38	27	number	number	NOUN
ejpam-5895	38	28	of	of	ADP
ejpam-5895	38	29	smaller	small	ADJ
ejpam-5895	38	30	areas	area	NOUN
ejpam-5895	38	31	known	know	VERB
ejpam-5895	38	32	as	as	ADP
ejpam-5895	38	33	elements	element	NOUN
ejpam-5895	38	34	.	.	PUNCT
ejpam-5895	39	1	nowadays	nowadays	ADV
ejpam-5895	39	2	,	,	PUNCT
ejpam-5895	39	3	a	a	DET
ejpam-5895	39	4	lot	lot	NOUN
ejpam-5895	39	5	of	of	ADP
ejpam-5895	39	6	problems	problem	NOUN
ejpam-5895	39	7	in	in	ADP
ejpam-5895	39	8	multiphysics	multiphysic	NOUN
ejpam-5895	39	9	,	,	PUNCT
ejpam-5895	39	10	fluids	fluid	NOUN
ejpam-5895	39	11	,	,	PUNCT
ejpam-5895	39	12	and	and	CCONJ
ejpam-5895	39	13	structures	structure	NOUN
ejpam-5895	39	14	are	be	AUX
ejpam-5895	39	15	solved	solve	VERB
ejpam-5895	39	16	numerically	numerically	ADV
ejpam-5895	39	17	using	use	VERB
ejpam-5895	39	18	fems	fem	NOUN
ejpam-5895	39	19	.	.	PUNCT
ejpam-5895	40	1	because	because	SCONJ
ejpam-5895	40	2	scientists	scientist	NOUN
ejpam-5895	40	3	and	and	CCONJ
ejpam-5895	40	4	engineers	engineer	NOUN
ejpam-5895	40	5	can	can	AUX
ejpam-5895	40	6	model	model	VERB
ejpam-5895	40	7	and	and	CCONJ
ejpam-5895	40	8	solve	solve	VERB
ejpam-5895	40	9	extremely	extremely	ADV
ejpam-5895	40	10	complicated	complicated	ADJ
ejpam-5895	40	11	problems	problem	NOUN
ejpam-5895	40	12	numerically	numerically	ADV
ejpam-5895	40	13	and	and	CCONJ
ejpam-5895	40	14	mathematically	mathematically	ADV
ejpam-5895	40	15	,	,	PUNCT
ejpam-5895	40	16	the	the	DET
ejpam-5895	40	17	approach	approach	NOUN
ejpam-5895	40	18	is	be	AUX
ejpam-5895	40	19	widely	widely	ADV
ejpam-5895	40	20	used	use	VERB
ejpam-5895	40	21	[	[	PUNCT
ejpam-5895	40	22	8–10	8–10	NOUN
ejpam-5895	40	23	]	]	PUNCT
ejpam-5895	40	24	.	.	PUNCT
ejpam-5895	41	1	engineering	engineering	NOUN
ejpam-5895	41	2	analyses	analysis	NOUN
ejpam-5895	41	3	are	be	AUX
ejpam-5895	41	4	used	use	VERB
ejpam-5895	41	5	to	to	PART
ejpam-5895	41	6	evaluate	evaluate	VERB
ejpam-5895	41	7	designs	design	NOUN
ejpam-5895	41	8	,	,	PUNCT
ejpam-5895	41	9	while	while	SCONJ
ejpam-5895	41	10	scientific	scientific	ADJ
ejpam-5895	41	11	analyses	analysis	NOUN
ejpam-5895	41	12	are	be	AUX
ejpam-5895	41	13	conducted	conduct	VERB
ejpam-5895	41	14	primarily	primarily	ADV
ejpam-5895	41	15	to	to	PART
ejpam-5895	41	16	gain	gain	VERB
ejpam-5895	41	17	an	an	DET
ejpam-5895	41	18	understanding	understanding	NOUN
ejpam-5895	41	19	of	of	ADP
ejpam-5895	41	20	and	and	CCONJ
ejpam-5895	41	21	,	,	PUNCT
ejpam-5895	41	22	ideally	ideally	ADV
ejpam-5895	41	23	,	,	PUNCT
ejpam-5895	41	24	forecast	forecast	VERB
ejpam-5895	41	25	natural	natural	ADJ
ejpam-5895	41	26	events	event	NOUN
ejpam-5895	41	27	.	.	PUNCT
ejpam-5895	42	1	it	it	PRON
ejpam-5895	42	2	is	be	AUX
ejpam-5895	42	3	very	very	ADV
ejpam-5895	42	4	valuable	valuable	ADJ
ejpam-5895	42	5	to	to	PART
ejpam-5895	42	6	forecast	forecast	VERB
ejpam-5895	42	7	how	how	SCONJ
ejpam-5895	42	8	a	a	DET
ejpam-5895	42	9	design	design	NOUN
ejpam-5895	42	10	will	will	AUX
ejpam-5895	42	11	work	work	VERB
ejpam-5895	42	12	and	and	CCONJ
ejpam-5895	42	13	whether	whether	SCONJ
ejpam-5895	42	14	and	and	CCONJ
ejpam-5895	42	15	how	how	SCONJ
ejpam-5895	42	16	a	a	DET
ejpam-5895	42	17	natural	natural	ADJ
ejpam-5895	42	18	occurrence	occurrence	NOUN
ejpam-5895	42	19	will	will	AUX
ejpam-5895	42	20	occur	occur	VERB
ejpam-5895	42	21	.	.	PUNCT
ejpam-5895	43	1	by	by	ADP
ejpam-5895	43	2	doing	do	VERB
ejpam-5895	43	3	so	so	ADV
ejpam-5895	43	4	,	,	PUNCT
ejpam-5895	43	5	designs	design	NOUN
ejpam-5895	43	6	can	can	AUX
ejpam-5895	43	7	be	be	AUX
ejpam-5895	43	8	made	make	VERB
ejpam-5895	43	9	safer	safe	ADJ
ejpam-5895	43	10	and	and	CCONJ
ejpam-5895	43	11	more	more	ADV
ejpam-5895	43	12	economical	economical	ADJ
ejpam-5895	43	13	,	,	PUNCT
ejpam-5895	43	14	and	and	CCONJ
ejpam-5895	43	15	knowledge	knowledge	NOUN
ejpam-5895	43	16	of	of	ADP
ejpam-5895	43	17	the	the	DET
ejpam-5895	43	18	ability	ability	NOUN
ejpam-5895	43	19	to	to	PART
ejpam-5895	43	20	predict	predict	VERB
ejpam-5895	43	21	nature	nature	NOUN
ejpam-5895	43	22	can	can	AUX
ejpam-5895	43	23	assist	assist	VERB
ejpam-5895	43	24	,	,	PUNCT
ejpam-5895	43	25	for	for	ADP
ejpam-5895	43	26	instance	instance	NOUN
ejpam-5895	43	27	,	,	PUNCT
ejpam-5895	43	28	in	in	ADP
ejpam-5895	43	29	preventing	prevent	VERB
ejpam-5895	43	30	tragedies	tragedy	NOUN
ejpam-5895	43	31	.	.	PUNCT
ejpam-5895	44	1	therefore	therefore	ADV
ejpam-5895	44	2	,	,	PUNCT
ejpam-5895	44	3	using	use	VERB
ejpam-5895	44	4	the	the	DET
ejpam-5895	44	5	fem	fem	NOUN
ejpam-5895	44	6	significantly	significantly	ADV
ejpam-5895	44	7	improves	improve	VERB
ejpam-5895	44	8	our	our	PRON
ejpam-5895	44	9	quality	quality	NOUN
ejpam-5895	44	10	of	of	ADP
ejpam-5895	44	11	life	life	NOUN
ejpam-5895	44	12	[	[	X
ejpam-5895	44	13	11–13	11–13	NUM
ejpam-5895	44	14	]	]	X
ejpam-5895	44	15	.	.	PUNCT
ejpam-5895	45	1	the	the	DET
ejpam-5895	45	2	galerkin	galerkin	PROPN
ejpam-5895	45	3	finite	finite	PROPN
ejpam-5895	45	4	element	element	NOUN
ejpam-5895	45	5	method	method	NOUN
ejpam-5895	45	6	(	(	PUNCT
ejpam-5895	45	7	gfem	gfem	NOUN
ejpam-5895	45	8	)	)	PUNCT
ejpam-5895	45	9	divides	divide	VERB
ejpam-5895	45	10	the	the	DET
ejpam-5895	45	11	domain	domain	NOUN
ejpam-5895	45	12	into	into	ADP
ejpam-5895	45	13	finite	finite	ADJ
ejpam-5895	45	14	elements	element	NOUN
ejpam-5895	45	15	in	in	ADP
ejpam-5895	45	16	order	order	NOUN
ejpam-5895	45	17	to	to	PART
ejpam-5895	45	18	produce	produce	VERB
ejpam-5895	45	19	a	a	DET
ejpam-5895	45	20	numerical	numerical	ADJ
ejpam-5895	45	21	solution	solution	NOUN
ejpam-5895	45	22	to	to	ADP
ejpam-5895	45	23	a	a	DET
ejpam-5895	45	24	differential	differential	ADJ
ejpam-5895	45	25	equation	equation	NOUN
ejpam-5895	45	26	.	.	PUNCT
ejpam-5895	46	1	piecewise	piecewise	NOUN
ejpam-5895	46	2	trial	trial	NOUN
ejpam-5895	46	3	functions	function	NOUN
ejpam-5895	46	4	over	over	ADP
ejpam-5895	46	5	each	each	PRON
ejpam-5895	46	6	of	of	ADP
ejpam-5895	46	7	these	these	DET
ejpam-5895	46	8	elements	element	NOUN
ejpam-5895	46	9	are	be	AUX
ejpam-5895	46	10	used	use	VERB
ejpam-5895	46	11	to	to	PART
ejpam-5895	46	12	approximate	approximate	VERB
ejpam-5895	46	13	the	the	DET
ejpam-5895	46	14	function	function	NOUN
ejpam-5895	46	15	.	.	PUNCT
ejpam-5895	47	1	the	the	DET
ejpam-5895	47	2	gfem	gfem	NOUN
ejpam-5895	47	3	for	for	ADP
ejpam-5895	47	4	the	the	DET
ejpam-5895	47	5	solution	solution	NOUN
ejpam-5895	47	6	of	of	ADP
ejpam-5895	47	7	a	a	DET
ejpam-5895	47	8	differential	differential	ADJ
ejpam-5895	47	9	equation	equation	NOUN
ejpam-5895	47	10	consists	consist	VERB
ejpam-5895	47	11	of	of	ADP
ejpam-5895	47	12	the	the	DET
ejpam-5895	47	13	following	follow	VERB
ejpam-5895	47	14	steps	step	NOUN
ejpam-5895	47	15	[	[	X
ejpam-5895	47	16	14	14	NUM
ejpam-5895	47	17	,	,	PUNCT
ejpam-5895	47	18	15	15	NUM
ejpam-5895	47	19	]	]	SYM
ejpam-5895	47	20	:	:	PUNCT
ejpam-5895	47	21	1	1	NUM
ejpam-5895	47	22	multiply	multiply	VERB
ejpam-5895	47	23	the	the	DET
ejpam-5895	47	24	differential	differential	ADJ
ejpam-5895	47	25	equation	equation	NOUN
ejpam-5895	47	26	by	by	ADP
ejpam-5895	47	27	a	a	DET
ejpam-5895	47	28	weight	weight	NOUN
ejpam-5895	47	29	function	function	NOUN
ejpam-5895	47	30	ω(x	ω(x	NOUN
ejpam-5895	47	31	)	)	PUNCT
ejpam-5895	47	32	and	and	CCONJ
ejpam-5895	47	33	form	form	VERB
ejpam-5895	47	34	the	the	DET
ejpam-5895	47	35	integral	integral	ADJ
ejpam-5895	47	36	over	over	ADP
ejpam-5895	47	37	the	the	DET
ejpam-5895	47	38	whole	whole	ADJ
ejpam-5895	47	39	domain	domain	NOUN
ejpam-5895	47	40	.	.	PUNCT
ejpam-5895	48	1	s.	s.	PROPN
ejpam-5895	48	2	s.	s.	PROPN
ejpam-5895	48	3	almutairi	almutairi	PROPN
ejpam-5895	48	4	,	,	PUNCT
ejpam-5895	48	5	a.	a.	PROPN
ejpam-5895	48	6	m.	m.	PROPN
ejpam-5895	48	7	saeed	saeed	PROPN
ejpam-5895	48	8	/	/	SYM
ejpam-5895	48	9	eur	eur	PROPN
ejpam-5895	48	10	.	.	PUNCT
ejpam-5895	49	1	j.	j.	PROPN
ejpam-5895	49	2	pure	pure	PROPN
ejpam-5895	49	3	appl	appl	PROPN
ejpam-5895	49	4	.	.	PROPN
ejpam-5895	49	5	math	math	PROPN
ejpam-5895	49	6	,	,	PUNCT
ejpam-5895	49	7	18	18	NUM
ejpam-5895	49	8	(	(	PUNCT
ejpam-5895	49	9	2	2	NUM
ejpam-5895	49	10	)	)	PUNCT
ejpam-5895	49	11	(	(	PUNCT
ejpam-5895	49	12	2025	2025	NUM
ejpam-5895	49	13	)	)	PUNCT
ejpam-5895	49	14	,	,	PUNCT
ejpam-5895	49	15	5895	5895	NUM
ejpam-5895	49	16	3	3	NUM
ejpam-5895	49	17	of	of	ADP
ejpam-5895	49	18	10	10	NUM
ejpam-5895	49	19	2	2	NUM
ejpam-5895	49	20	if	if	SCONJ
ejpam-5895	49	21	necessary	necessary	ADJ
ejpam-5895	49	22	,	,	PUNCT
ejpam-5895	49	23	integrate	integrate	VERB
ejpam-5895	49	24	by	by	ADP
ejpam-5895	49	25	parts	part	NOUN
ejpam-5895	49	26	to	to	PART
ejpam-5895	49	27	reduce	reduce	VERB
ejpam-5895	49	28	the	the	DET
ejpam-5895	49	29	order	order	NOUN
ejpam-5895	49	30	of	of	ADP
ejpam-5895	49	31	the	the	DET
ejpam-5895	49	32	highest	high	ADJ
ejpam-5895	49	33	order	order	NOUN
ejpam-5895	49	34	term	term	NOUN
ejpam-5895	49	35	.	.	PUNCT
ejpam-5895	50	1	3	3	NUM
ejpam-5895	50	2	choose	choose	VERB
ejpam-5895	50	3	the	the	DET
ejpam-5895	50	4	order	order	NOUN
ejpam-5895	50	5	of	of	ADP
ejpam-5895	50	6	interpolation	interpolation	NOUN
ejpam-5895	50	7	(	(	PUNCT
ejpam-5895	50	8	e.g.	e.g.	ADV
ejpam-5895	50	9	linear	linear	ADJ
ejpam-5895	50	10	,	,	PUNCT
ejpam-5895	50	11	quadratic	quadratic	ADJ
ejpam-5895	50	12	,	,	PUNCT
ejpam-5895	50	13	etc	etc	X
ejpam-5895	50	14	.	.	X
ejpam-5895	50	15	)	)	PUNCT
ejpam-5895	51	1	and	and	CCONJ
ejpam-5895	51	2	corresponding	corresponding	ADJ
ejpam-5895	51	3	shape	shape	NOUN
ejpam-5895	51	4	functions	function	NOUN
ejpam-5895	51	5	ni	ni	PROPN
ejpam-5895	51	6	,	,	PUNCT
ejpam-5895	51	7	i	i	NOUN
ejpam-5895	51	8	=	=	NOUN
ejpam-5895	51	9	1	1	NUM
ejpam-5895	51	10	...	...	SYM
ejpam-5895	51	11	m	m	VERB
ejpam-5895	51	12	,	,	PUNCT
ejpam-5895	51	13	with	with	ADP
ejpam-5895	51	14	trial	trial	NOUN
ejpam-5895	51	15	function	function	NOUN
ejpam-5895	51	16	p	p	X
ejpam-5895	51	17	=	=	SYM
ejpam-5895	51	18	p̃(x	p̃(x	PROPN
ejpam-5895	51	19	)	)	PUNCT
ejpam-5895	51	20	=	=	PUNCT
ejpam-5895	52	1	m∑	m∑	INTJ
ejpam-5895	52	2	i=1	i=1	PROPN
ejpam-5895	52	3	ni(x)pi	ni(x)pi	ADJ
ejpam-5895	52	4	.	.	PUNCT
ejpam-5895	53	1	4	4	NUM
ejpam-5895	53	2	evaluate	evaluate	VERB
ejpam-5895	53	3	all	all	DET
ejpam-5895	53	4	integrals	integral	NOUN
ejpam-5895	53	5	over	over	ADP
ejpam-5895	53	6	each	each	DET
ejpam-5895	53	7	element	element	NOUN
ejpam-5895	53	8	,	,	PUNCT
ejpam-5895	53	9	either	either	CCONJ
ejpam-5895	53	10	exactly	exactly	ADV
ejpam-5895	53	11	or	or	CCONJ
ejpam-5895	53	12	numerically	numerically	ADV
ejpam-5895	53	13	,	,	PUNCT
ejpam-5895	53	14	to	to	PART
ejpam-5895	53	15	set	set	VERB
ejpam-5895	53	16	up	up	ADP
ejpam-5895	53	17	a	a	DET
ejpam-5895	53	18	system	system	NOUN
ejpam-5895	53	19	of	of	ADP
ejpam-5895	53	20	equations	equation	NOUN
ejpam-5895	53	21	in	in	ADP
ejpam-5895	53	22	the	the	DET
ejpam-5895	53	23	unknown	unknown	ADJ
ejpam-5895	53	24	pi′s	pi′s	NOUN
ejpam-5895	53	25	.	.	PUNCT
ejpam-5895	54	1	5	5	NUM
ejpam-5895	54	2	solve	solve	VERB
ejpam-5895	54	3	the	the	DET
ejpam-5895	54	4	system	system	NOUN
ejpam-5895	54	5	of	of	ADP
ejpam-5895	54	6	equations	equation	NOUN
ejpam-5895	54	7	for	for	ADP
ejpam-5895	54	8	the	the	DET
ejpam-5895	54	9	pi′s	pi′s	NOUN
ejpam-5895	54	10	.	.	PUNCT
ejpam-5895	55	1	this	this	DET
ejpam-5895	55	2	work	work	NOUN
ejpam-5895	55	3	will	will	AUX
ejpam-5895	55	4	be	be	AUX
ejpam-5895	55	5	focus	focus	VERB
ejpam-5895	55	6	on	on	ADP
ejpam-5895	55	7	the	the	DET
ejpam-5895	55	8	applications	application	NOUN
ejpam-5895	55	9	of	of	ADP
ejpam-5895	55	10	gfem	gfem	NOUN
ejpam-5895	55	11	and	and	CCONJ
ejpam-5895	55	12	compare	compare	VERB
ejpam-5895	55	13	it	it	PRON
ejpam-5895	55	14	with	with	ADP
ejpam-5895	55	15	the	the	DET
ejpam-5895	55	16	fdm	fdm	NOUN
ejpam-5895	55	17	to	to	PART
ejpam-5895	55	18	check	check	VERB
ejpam-5895	55	19	more	more	ADJ
ejpam-5895	55	20	superiority	superiority	NOUN
ejpam-5895	55	21	method	method	NOUN
ejpam-5895	55	22	.	.	PUNCT
ejpam-5895	56	1	this	this	DET
ejpam-5895	56	2	paper	paper	NOUN
ejpam-5895	56	3	organized	organize	VERB
ejpam-5895	56	4	5	5	NUM
ejpam-5895	56	5	sections	section	NOUN
ejpam-5895	56	6	.	.	PUNCT
ejpam-5895	57	1	section	section	NOUN
ejpam-5895	57	2	2	2	NUM
ejpam-5895	57	3	,	,	PUNCT
ejpam-5895	57	4	introduced	introduce	VERB
ejpam-5895	57	5	a	a	DET
ejpam-5895	57	6	brief	brief	ADJ
ejpam-5895	57	7	description	description	NOUN
ejpam-5895	57	8	of	of	ADP
ejpam-5895	57	9	the	the	DET
ejpam-5895	57	10	fdm	fdm	NOUN
ejpam-5895	57	11	.	.	PUNCT
ejpam-5895	58	1	section	section	NOUN
ejpam-5895	58	2	3	3	NUM
ejpam-5895	58	3	,	,	PUNCT
ejpam-5895	58	4	presented	present	VERB
ejpam-5895	58	5	the	the	DET
ejpam-5895	58	6	formulations	formulation	NOUN
ejpam-5895	58	7	of	of	ADP
ejpam-5895	58	8	the	the	DET
ejpam-5895	58	9	gfem	gfem	NOUN
ejpam-5895	58	10	for	for	ADP
ejpam-5895	58	11	solving	solve	VERB
ejpam-5895	58	12	pdes	pde	NOUN
ejpam-5895	58	13	of	of	ADP
ejpam-5895	58	14	elliptic	elliptic	ADJ
ejpam-5895	58	15	type	type	NOUN
ejpam-5895	58	16	.	.	PUNCT
ejpam-5895	59	1	section	section	NOUN
ejpam-5895	59	2	4	4	NUM
ejpam-5895	59	3	includes	include	VERB
ejpam-5895	59	4	the	the	DET
ejpam-5895	59	5	numerical	numerical	ADJ
ejpam-5895	59	6	experiments	experiment	NOUN
ejpam-5895	59	7	and	and	CCONJ
ejpam-5895	59	8	the	the	DET
ejpam-5895	59	9	comparison	comparison	NOUN
ejpam-5895	59	10	between	between	ADP
ejpam-5895	59	11	these	these	DET
ejpam-5895	59	12	two	two	NUM
ejpam-5895	59	13	method	method	NOUN
ejpam-5895	59	14	.	.	PUNCT
ejpam-5895	60	1	the	the	DET
ejpam-5895	60	2	paper	paper	NOUN
ejpam-5895	60	3	ends	end	VERB
ejpam-5895	60	4	with	with	ADP
ejpam-5895	60	5	conclusion	conclusion	NOUN
ejpam-5895	60	6	and	and	CCONJ
ejpam-5895	60	7	final	final	ADJ
ejpam-5895	60	8	remarks	remark	NOUN
ejpam-5895	60	9	.	.	PUNCT
ejpam-5895	61	1	2	2	X
ejpam-5895	61	2	.	.	X
ejpam-5895	61	3	finite	finite	ADJ
ejpam-5895	61	4	difference	difference	NOUN
ejpam-5895	61	5	method	method	NOUN
ejpam-5895	61	6	the	the	DET
ejpam-5895	61	7	poisson	poisson	NOUN
ejpam-5895	61	8	’s	’s	PART
ejpam-5895	61	9	equation	equation	NOUN
ejpam-5895	61	10	in	in	ADP
ejpam-5895	61	11	two	two	NUM
ejpam-5895	61	12	-	-	PUNCT
ejpam-5895	61	13	dimension	dimension	NOUN
ejpam-5895	61	14	can	can	AUX
ejpam-5895	61	15	be	be	AUX
ejpam-5895	61	16	written	write	VERB
ejpam-5895	61	17	as	as	ADP
ejpam-5895	61	18	[	[	X
ejpam-5895	61	19	16–18	16–18	NUM
ejpam-5895	61	20	]	]	PUNCT
ejpam-5895	61	21	.	.	PUNCT
ejpam-5895	62	1	∂2u	∂2u	PROPN
ejpam-5895	62	2	∂x2	∂x2	PROPN
ejpam-5895	62	3	+	+	CCONJ
ejpam-5895	62	4	∂2u	∂2u	ADJ
ejpam-5895	62	5	∂y2	∂y2	NOUN
ejpam-5895	62	6	=	=	SYM
ejpam-5895	62	7	g(x	g(x	PROPN
ejpam-5895	62	8	,	,	PUNCT
ejpam-5895	62	9	y	y	NOUN
ejpam-5895	62	10	)	)	PUNCT
ejpam-5895	62	11	(	(	PUNCT
ejpam-5895	62	12	1	1	X
ejpam-5895	62	13	)	)	PUNCT
ejpam-5895	62	14	along	along	ADP
ejpam-5895	62	15	the	the	DET
ejpam-5895	62	16	boundary	boundary	ADJ
ejpam-5895	62	17	c	c	NOUN
ejpam-5895	62	18	with	with	ADP
ejpam-5895	62	19	the	the	DET
ejpam-5895	62	20	boundary	boundary	ADJ
ejpam-5895	62	21	condition	condition	NOUN
ejpam-5895	62	22	u	u	NOUN
ejpam-5895	62	23	=	=	PROPN
ejpam-5895	62	24	f(x	f(x	PROPN
ejpam-5895	62	25	,	,	PUNCT
ejpam-5895	62	26	y	y	PROPN
ejpam-5895	62	27	)	)	PUNCT
ejpam-5895	62	28	.	.	PUNCT
ejpam-5895	63	1	here	here	ADV
ejpam-5895	63	2	,	,	PUNCT
ejpam-5895	63	3	we	we	PRON
ejpam-5895	63	4	also	also	ADV
ejpam-5895	63	5	made	make	VERB
ejpam-5895	63	6	the	the	DET
ejpam-5895	63	7	assumption	assumption	NOUN
ejpam-5895	63	8	that	that	SCONJ
ejpam-5895	63	9	the	the	DET
ejpam-5895	63	10	mesh	mesh	NOUN
ejpam-5895	63	11	points	point	NOUN
ejpam-5895	63	12	are	be	AUX
ejpam-5895	63	13	uniform	uniform	ADJ
ejpam-5895	63	14	in	in	ADP
ejpam-5895	63	15	both	both	CCONJ
ejpam-5895	63	16	the	the	DET
ejpam-5895	63	17	x	x	X
ejpam-5895	63	18	and	and	CCONJ
ejpam-5895	63	19	y	y	PROPN
ejpam-5895	63	20	dimensions	dimension	NOUN
ejpam-5895	63	21	.	.	PUNCT
ejpam-5895	64	1	with	with	ADP
ejpam-5895	64	2	this	this	DET
ejpam-5895	64	3	presumption	presumption	NOUN
ejpam-5895	64	4	,	,	PUNCT
ejpam-5895	64	5	the	the	DET
ejpam-5895	64	6	equation	equation	NOUN
ejpam-5895	64	7	(	(	PUNCT
ejpam-5895	64	8	1	1	X
ejpam-5895	64	9	)	)	PUNCT
ejpam-5895	64	10	central	central	ADJ
ejpam-5895	64	11	difference	difference	NOUN
ejpam-5895	64	12	approximation	approximation	NOUN
ejpam-5895	64	13	can	can	AUX
ejpam-5895	64	14	be	be	AUX
ejpam-5895	64	15	simplified	simplify	VERB
ejpam-5895	64	16	to	to	ADP
ejpam-5895	64	17	ui	ui	PROPN
ejpam-5895	64	18	,	,	PUNCT
ejpam-5895	64	19	j	j	PROPN
ejpam-5895	65	1	=	=	NOUN
ejpam-5895	65	2	1	1	NUM
ejpam-5895	65	3	4	4	NUM
ejpam-5895	65	4	(	(	PUNCT
ejpam-5895	65	5	ui+1,j	ui+1,j	NOUN
ejpam-5895	65	6	+	+	CCONJ
ejpam-5895	65	7	ui−1,j	ui−1,j	X
ejpam-5895	65	8	+	+	CCONJ
ejpam-5895	65	9	ui	ui	NOUN
ejpam-5895	65	10	,	,	PUNCT
ejpam-5895	65	11	j+1	j+1	PROPN
ejpam-5895	65	12	+	+	PROPN
ejpam-5895	65	13	ui	ui	NOUN
ejpam-5895	65	14	,	,	PUNCT
ejpam-5895	65	15	j−1	j−1	PROPN
ejpam-5895	65	16	−	−	PROPN
ejpam-5895	65	17	h2gi	h2gi	PROPN
ejpam-5895	65	18	,	,	PUNCT
ejpam-5895	65	19	j	j	NOUN
ejpam-5895	65	20	)	)	PUNCT
ejpam-5895	65	21	where	where	SCONJ
ejpam-5895	65	22	gi	gi	ADP
ejpam-5895	65	23	,	,	PUNCT
ejpam-5895	65	24	j	j	PROPN
ejpam-5895	65	25	=	=	SYM
ejpam-5895	65	26	g(xi	g(xi	PROPN
ejpam-5895	65	27	,	,	PUNCT
ejpam-5895	65	28	yi	yi	PROPN
ejpam-5895	65	29	)	)	PUNCT
ejpam-5895	65	30	.	.	PUNCT
ejpam-5895	66	1	this	this	DET
ejpam-5895	66	2	formula	formula	NOUN
ejpam-5895	66	3	is	be	AUX
ejpam-5895	66	4	known	know	VERB
ejpam-5895	66	5	as	as	ADP
ejpam-5895	66	6	standard	standard	ADJ
ejpam-5895	66	7	five	five	NUM
ejpam-5895	66	8	-	-	PUNCT
ejpam-5895	66	9	point	point	NOUN
ejpam-5895	66	10	formula	formula	NOUN
ejpam-5895	66	11	.	.	PUNCT
ejpam-5895	67	1	let	let	VERB
ejpam-5895	67	2	u	u	NOUN
ejpam-5895	67	3	=	=	NOUN
ejpam-5895	67	4	0	0	NUM
ejpam-5895	67	5	along	along	ADP
ejpam-5895	67	6	the	the	DET
ejpam-5895	67	7	boundary	boundary	ADJ
ejpam-5895	67	8	c	c	PROPN
ejpam-5895	67	9	and	and	CCONJ
ejpam-5895	67	10	i	i	PROPN
ejpam-5895	67	11	,	,	PUNCT
ejpam-5895	67	12	j	j	PROPN
ejpam-5895	67	13	=	=	SYM
ejpam-5895	67	14	0	0	NUM
ejpam-5895	67	15	,	,	PUNCT
ejpam-5895	67	16	1	1	NUM
ejpam-5895	67	17	,	,	PUNCT
ejpam-5895	67	18	2	2	NUM
ejpam-5895	67	19	,	,	PUNCT
ejpam-5895	67	20	3	3	NUM
ejpam-5895	67	21	,	,	PUNCT
ejpam-5895	67	22	4	4	NUM
ejpam-5895	67	23	.	.	PUNCT
ejpam-5895	68	1	then	then	ADV
ejpam-5895	68	2	u0,j	u0,j	PROPN
ejpam-5895	68	3	=	=	SYM
ejpam-5895	68	4	0	0	NUM
ejpam-5895	68	5	,	,	PUNCT
ejpam-5895	68	6	u4,j	u4,j	PROPN
ejpam-5895	68	7	=	=	SYM
ejpam-5895	68	8	0	0	NUM
ejpam-5895	68	9	,	,	PUNCT
ejpam-5895	68	10	for	for	ADP
ejpam-5895	68	11	j	j	PROPN
ejpam-5895	68	12	=	=	SYM
ejpam-5895	68	13	0	0	PROPN
ejpam-5895	68	14	,	,	PUNCT
ejpam-5895	68	15	1	1	NUM
ejpam-5895	68	16	,	,	PUNCT
ejpam-5895	68	17	2	2	NUM
ejpam-5895	68	18	,	,	PUNCT
ejpam-5895	68	19	3	3	NUM
ejpam-5895	68	20	,	,	PUNCT
ejpam-5895	68	21	4.and	4.and	NOUN
ejpam-5895	68	22	ui,0	ui,0	PROPN
ejpam-5895	68	23	=	=	SYM
ejpam-5895	68	24	0	0	NUM
ejpam-5895	68	25	,	,	PUNCT
ejpam-5895	68	26	ui,4	ui,4	PROPN
ejpam-5895	68	27	=	=	NOUN
ejpam-5895	68	28	0	0	NUM
ejpam-5895	68	29	for	for	ADP
ejpam-5895	68	30	i	i	PRON
ejpam-5895	68	31	=	=	SYM
ejpam-5895	68	32	0	0	NUM
ejpam-5895	68	33	,	,	PUNCT
ejpam-5895	68	34	1	1	NUM
ejpam-5895	68	35	,	,	PUNCT
ejpam-5895	68	36	2	2	NUM
ejpam-5895	68	37	,	,	PUNCT
ejpam-5895	68	38	3	3	NUM
ejpam-5895	68	39	,	,	PUNCT
ejpam-5895	68	40	4	4	NUM
ejpam-5895	68	41	.	.	PUNCT
ejpam-5895	69	1	the	the	DET
ejpam-5895	69	2	boundary	boundary	ADJ
ejpam-5895	69	3	values	value	NOUN
ejpam-5895	69	4	(	(	PUNCT
ejpam-5895	69	5	filled	fill	VERB
ejpam-5895	69	6	circles	circle	NOUN
ejpam-5895	69	7	)	)	PUNCT
ejpam-5895	69	8	are	be	AUX
ejpam-5895	69	9	shown	show	VERB
ejpam-5895	69	10	in	in	ADP
ejpam-5895	69	11	figure	figure	NOUN
ejpam-5895	69	12	1	1	NUM
ejpam-5895	69	13	.	.	PUNCT
ejpam-5895	69	14	s.	s.	PROPN
ejpam-5895	69	15	s.	s.	PROPN
ejpam-5895	69	16	almutairi	almutairi	PROPN
ejpam-5895	69	17	,	,	PUNCT
ejpam-5895	69	18	a.	a.	PROPN
ejpam-5895	69	19	m.	m.	PROPN
ejpam-5895	69	20	saeed	saeed	PROPN
ejpam-5895	69	21	/	/	SYM
ejpam-5895	69	22	eur	eur	PROPN
ejpam-5895	69	23	.	.	PUNCT
ejpam-5895	70	1	j.	j.	PROPN
ejpam-5895	70	2	pure	pure	PROPN
ejpam-5895	70	3	appl	appl	PROPN
ejpam-5895	70	4	.	.	PROPN
ejpam-5895	70	5	math	math	PROPN
ejpam-5895	70	6	,	,	PUNCT
ejpam-5895	70	7	18	18	NUM
ejpam-5895	70	8	(	(	PUNCT
ejpam-5895	70	9	2	2	NUM
ejpam-5895	70	10	)	)	PUNCT
ejpam-5895	70	11	(	(	PUNCT
ejpam-5895	70	12	2025	2025	NUM
ejpam-5895	70	13	)	)	PUNCT
ejpam-5895	70	14	,	,	PUNCT
ejpam-5895	70	15	5895	5895	NUM
ejpam-5895	70	16	4	4	NUM
ejpam-5895	70	17	of	of	ADP
ejpam-5895	70	18	10	10	NUM
ejpam-5895	70	19	figure	figure	NOUN
ejpam-5895	70	20	1	1	NUM
ejpam-5895	70	21	:	:	PUNCT
ejpam-5895	70	22	mesh	mesh	NOUN
ejpam-5895	70	23	points	point	NOUN
ejpam-5895	70	24	of	of	ADP
ejpam-5895	70	25	fdm	fdm	NOUN
ejpam-5895	70	26	.	.	PUNCT
ejpam-5895	71	1	for	for	ADP
ejpam-5895	71	2	a	a	DET
ejpam-5895	71	3	particular	particular	ADJ
ejpam-5895	71	4	case	case	NOUN
ejpam-5895	71	5	,	,	PUNCT
ejpam-5895	71	6	i.e.	i.e.	X
ejpam-5895	71	7	for	for	ADP
ejpam-5895	71	8	i	i	PROPN
ejpam-5895	71	9	,	,	PUNCT
ejpam-5895	71	10	j	j	PROPN
ejpam-5895	71	11	=	=	SYM
ejpam-5895	71	12	0	0	NUM
ejpam-5895	71	13	,	,	PUNCT
ejpam-5895	71	14	1	1	NUM
ejpam-5895	71	15	,	,	PUNCT
ejpam-5895	71	16	2	2	NUM
ejpam-5895	71	17	,	,	PUNCT
ejpam-5895	71	18	3	3	NUM
ejpam-5895	71	19	.	.	PUNCT
ejpam-5895	71	20	the	the	DET
ejpam-5895	71	21	equation	equation	NOUN
ejpam-5895	71	22	(	(	PUNCT
ejpam-5895	71	23	1	1	X
ejpam-5895	71	24	)	)	PUNCT
ejpam-5895	71	25	becomes	become	VERB
ejpam-5895	71	26	a	a	DET
ejpam-5895	71	27	system	system	NOUN
ejpam-5895	71	28	of	of	ADP
ejpam-5895	71	29	nine	nine	NUM
ejpam-5895	71	30	equations	equation	NOUN
ejpam-5895	71	31	with	with	ADP
ejpam-5895	71	32	nine	nine	NUM
ejpam-5895	71	33	unknowns	unknown	NOUN
ejpam-5895	71	34	.	.	PUNCT
ejpam-5895	72	1	these	these	DET
ejpam-5895	72	2	equations	equation	NOUN
ejpam-5895	72	3	are	be	AUX
ejpam-5895	72	4	written	write	VERB
ejpam-5895	72	5	in	in	ADP
ejpam-5895	72	6	matrix	matrix	NOUN
ejpam-5895	72	7	notation	notation	NOUN
ejpam-5895	72	8	as	as	NUM
ejpam-5895	72	9	4	4	NUM
ejpam-5895	72	10	−1	−1	NOUN
ejpam-5895	72	11	0	0	NUM
ejpam-5895	72	12	−1	−1	NOUN
ejpam-5895	72	13	0	0	NUM
ejpam-5895	72	14	0	0	NUM
ejpam-5895	72	15	0	0	NUM
ejpam-5895	72	16	0	0	NUM
ejpam-5895	72	17	0	0	NUM
ejpam-5895	72	18	−1	−1	NOUN
ejpam-5895	72	19	4	4	NUM
ejpam-5895	72	20	−1	−1	NOUN
ejpam-5895	72	21	0	0	NUM
ejpam-5895	72	22	−1	−1	NOUN
ejpam-5895	72	23	0	0	NUM
ejpam-5895	72	24	0	0	NUM
ejpam-5895	72	25	0	0	NUM
ejpam-5895	72	26	0	0	NUM
ejpam-5895	72	27	0	0	NUM
ejpam-5895	72	28	−1	−1	NOUN
ejpam-5895	72	29	4	4	NUM
ejpam-5895	72	30	0	0	NUM
ejpam-5895	72	31	0	0	NUM
ejpam-5895	72	32	−1	−1	NOUN
ejpam-5895	72	33	0	0	NUM
ejpam-5895	72	34	0	0	NUM
ejpam-5895	72	35	0	0	NUM
ejpam-5895	72	36	−1	−1	NOUN
ejpam-5895	72	37	0	0	NUM
ejpam-5895	72	38	0	0	NUM
ejpam-5895	72	39	4	4	NUM
ejpam-5895	72	40	−1	−1	NOUN
ejpam-5895	72	41	0	0	NUM
ejpam-5895	72	42	−1	−1	NOUN
ejpam-5895	72	43	0	0	NUM
ejpam-5895	72	44	0	0	NUM
ejpam-5895	72	45	0	0	NUM
ejpam-5895	72	46	−1	−1	NOUN
ejpam-5895	72	47	0	0	NUM
ejpam-5895	72	48	−1	−1	NOUN
ejpam-5895	72	49	4	4	NUM
ejpam-5895	72	50	−1	−1	NOUN
ejpam-5895	72	51	0	0	NUM
ejpam-5895	72	52	−1	−1	NOUN
ejpam-5895	72	53	0	0	NUM
ejpam-5895	72	54	0	0	NUM
ejpam-5895	72	55	0	0	NUM
ejpam-5895	72	56	−1	−1	NOUN
ejpam-5895	72	57	0	0	NUM
ejpam-5895	72	58	−1	−1	NOUN
ejpam-5895	72	59	4	4	NUM
ejpam-5895	72	60	0	0	NUM
ejpam-5895	72	61	0	0	NUM
ejpam-5895	72	62	−1	−1	NOUN
ejpam-5895	72	63	0	0	NUM
ejpam-5895	72	64	0	0	NUM
ejpam-5895	72	65	0	0	NUM
ejpam-5895	72	66	−1	−1	NOUN
ejpam-5895	72	67	0	0	NUM
ejpam-5895	72	68	0	0	NUM
ejpam-5895	72	69	4	4	NUM
ejpam-5895	72	70	−1	−1	NOUN
ejpam-5895	72	71	0	0	NUM
ejpam-5895	72	72	0	0	NUM
ejpam-5895	72	73	0	0	NUM
ejpam-5895	72	74	0	0	NUM
ejpam-5895	72	75	0	0	NUM
ejpam-5895	72	76	−1	−1	NOUN
ejpam-5895	72	77	0	0	NUM
ejpam-5895	72	78	−1	−1	NOUN
ejpam-5895	72	79	4	4	NUM
ejpam-5895	72	80	−1	−1	NOUN
ejpam-5895	72	81	0	0	NUM
ejpam-5895	72	82	0	0	NUM
ejpam-5895	72	83	0	0	NUM
ejpam-5895	72	84	0	0	NUM
ejpam-5895	72	85	0	0	NUM
ejpam-5895	72	86	−1	−1	NOUN
ejpam-5895	72	87	0	0	NUM
ejpam-5895	72	88	−1	−1	NOUN
ejpam-5895	72	89	4	4	NUM
ejpam-5895	72	90			NOUN
ejpam-5895	72	91			VERB
ejpam-5895	73	1	u1,1	u1,1	PROPN
ejpam-5895	73	2	u1,2	u1,2	ADJ
ejpam-5895	73	3	u1,3	u1,3	NOUN
ejpam-5895	73	4	u2,1	u2,1	PROPN
ejpam-5895	74	1	u2,2	u2,2	PROPN
ejpam-5895	74	2	u2,3	u2,3	ADJ
ejpam-5895	74	3	u3,1	u3,1	NOUN
ejpam-5895	74	4	u3,2	u3,2	ADJ
ejpam-5895	74	5	u3,3	u3,3	NOUN
ejpam-5895	74	6			NOUN
ejpam-5895	74	7	=	=	PRON
ejpam-5895	74	8			VERB
ejpam-5895	74	9	−h2g1,1	−h2g1,1	NUM
ejpam-5895	74	10	−h2g1,2	−h2g1,2	NOUN
ejpam-5895	74	11	−h2g1,3	−h2g1,3	NUM
ejpam-5895	74	12	−h2g2,1	−h2g2,1	PROPN
ejpam-5895	74	13	−h2g2,2	−h2g2,2	NUM
ejpam-5895	74	14	−h2g2,3	−h2g2,3	NUM
ejpam-5895	74	15	−h2g3,1	−h2g3,1	PROPN
ejpam-5895	74	16	−h2g3,2	−h2g3,2	NOUN
ejpam-5895	74	17	−h2g3,3	−h2g3,3	NUM
ejpam-5895	74	18			PROPN
ejpam-5895	74	19	as	as	ADP
ejpam-5895	74	20	a	a	DET
ejpam-5895	74	21	result	result	NOUN
ejpam-5895	74	22	,	,	PUNCT
ejpam-5895	74	23	equation	equation	NOUN
ejpam-5895	74	24	(	(	PUNCT
ejpam-5895	74	25	1	1	X
ejpam-5895	74	26	)	)	PUNCT
ejpam-5895	74	27	formed	form	VERB
ejpam-5895	74	28	a	a	DET
ejpam-5895	74	29	system	system	NOUN
ejpam-5895	74	30	of	of	ADP
ejpam-5895	74	31	n	n	DET
ejpam-5895	74	32	equations	equation	NOUN
ejpam-5895	74	33	,	,	PUNCT
ejpam-5895	74	34	where	where	SCONJ
ejpam-5895	74	35	n	n	PRON
ejpam-5895	74	36	is	be	AUX
ejpam-5895	74	37	the	the	DET
ejpam-5895	74	38	number	number	NOUN
ejpam-5895	74	39	of	of	ADP
ejpam-5895	74	40	subintervals	subinterval	NOUN
ejpam-5895	74	41	along	along	ADP
ejpam-5895	74	42	the	the	DET
ejpam-5895	74	43	x	x	NOUN
ejpam-5895	74	44	and	and	CCONJ
ejpam-5895	74	45	y	y	PROPN
ejpam-5895	74	46	axes	axis	NOUN
ejpam-5895	74	47	.	.	PUNCT
ejpam-5895	75	1	the	the	DET
ejpam-5895	75	2	coefficient	coefficient	NOUN
ejpam-5895	75	3	matrix	matrix	NOUN
ejpam-5895	75	4	is	be	AUX
ejpam-5895	75	5	symmetric	symmetric	ADJ
ejpam-5895	75	6	,	,	PUNCT
ejpam-5895	75	7	sparse	sparse	ADJ
ejpam-5895	75	8	(	(	PUNCT
ejpam-5895	75	9	many	many	ADJ
ejpam-5895	75	10	elements	element	NOUN
ejpam-5895	75	11	are	be	AUX
ejpam-5895	75	12	0	0	NUM
ejpam-5895	75	13	)	)	PUNCT
ejpam-5895	75	14	,	,	PUNCT
ejpam-5895	75	15	and	and	CCONJ
ejpam-5895	75	16	positive	positive	ADJ
ejpam-5895	75	17	definite	definite	ADJ
ejpam-5895	75	18	.	.	PUNCT
ejpam-5895	76	1	the	the	DET
ejpam-5895	76	2	preceding	precede	VERB
ejpam-5895	76	3	system	system	NOUN
ejpam-5895	76	4	of	of	ADP
ejpam-5895	76	5	equations	equation	NOUN
ejpam-5895	76	6	should	should	AUX
ejpam-5895	76	7	be	be	AUX
ejpam-5895	76	8	solved	solve	VERB
ejpam-5895	76	9	iteratively	iteratively	ADV
ejpam-5895	76	10	rather	rather	ADV
ejpam-5895	76	11	than	than	ADP
ejpam-5895	76	12	directly	directly	ADV
ejpam-5895	76	13	because	because	SCONJ
ejpam-5895	76	14	the	the	DET
ejpam-5895	76	15	coefficient	coefficient	NOUN
ejpam-5895	76	16	matrix	matrix	NOUN
ejpam-5895	76	17	is	be	AUX
ejpam-5895	76	18	sparse	sparse	ADJ
ejpam-5895	76	19	.	.	PUNCT
ejpam-5895	76	20	.	.	PUNCT
ejpam-5895	77	1	constructing	construct	VERB
ejpam-5895	77	2	exact	exact	ADJ
ejpam-5895	77	3	and	and	CCONJ
ejpam-5895	77	4	numerical	numerical	ADJ
ejpam-5895	77	5	solutions	solution	NOUN
ejpam-5895	77	6	of	of	ADP
ejpam-5895	77	7	partial	partial	ADJ
ejpam-5895	77	8	differential	differential	ADJ
ejpam-5895	77	9	equations	equation	NOUN
ejpam-5895	77	10	(	(	PUNCT
ejpam-5895	77	11	pdes	pde	NOUN
ejpam-5895	77	12	)	)	PUNCT
ejpam-5895	77	13	has	have	AUX
ejpam-5895	77	14	become	become	VERB
ejpam-5895	77	15	an	an	DET
ejpam-5895	77	16	active	active	ADJ
ejpam-5895	77	17	area	area	NOUN
ejpam-5895	77	18	in	in	ADP
ejpam-5895	77	19	recent	recent	ADJ
ejpam-5895	77	20	years	year	NOUN
ejpam-5895	77	21	.	.	PUNCT
ejpam-5895	78	1	several	several	ADJ
ejpam-5895	78	2	applications	application	NOUN
ejpam-5895	78	3	of	of	ADP
ejpam-5895	78	4	pdes	pde	NOUN
ejpam-5895	78	5	have	have	AUX
ejpam-5895	78	6	been	be	AUX
ejpam-5895	78	7	developed	develop	VERB
ejpam-5895	78	8	over	over	ADP
ejpam-5895	78	9	the	the	DET
ejpam-5895	78	10	years	year	NOUN
ejpam-5895	78	11	,	,	PUNCT
ejpam-5895	78	12	such	such	ADJ
ejpam-5895	78	13	as	as	ADP
ejpam-5895	78	14	in	in	ADP
ejpam-5895	78	15	the	the	DET
ejpam-5895	78	16	theory	theory	NOUN
ejpam-5895	78	17	of	of	ADP
ejpam-5895	78	18	heat	heat	NOUN
ejpam-5895	78	19	-	-	PUNCT
ejpam-5895	78	20	magneto	magneto	NOUN
ejpam-5895	78	21	-	-	PUNCT
ejpam-5895	78	22	photothermal	photothermal	ADJ
ejpam-5895	78	23	and	and	CCONJ
ejpam-5895	78	24	magnetic	magnetic	ADJ
ejpam-5895	78	25	fields	field	NOUN
ejpam-5895	78	26	.	.	PUNCT
ejpam-5895	79	1	there	there	PRON
ejpam-5895	79	2	are	be	VERB
ejpam-5895	79	3	many	many	ADJ
ejpam-5895	79	4	complex	complex	ADJ
ejpam-5895	79	5	problems	problem	NOUN
ejpam-5895	79	6	in	in	ADP
ejpam-5895	79	7	mathematics	mathematics	PROPN
ejpam-5895	79	8	and	and	CCONJ
ejpam-5895	79	9	physics	physic	NOUN
ejpam-5895	79	10	that	that	PRON
ejpam-5895	79	11	involve	involve	VERB
ejpam-5895	79	12	the	the	DET
ejpam-5895	79	13	use	use	NOUN
ejpam-5895	79	14	of	of	ADP
ejpam-5895	79	15	pdes	pde	NOUN
ejpam-5895	79	16	.	.	PUNCT
ejpam-5895	80	1	these	these	DET
ejpam-5895	80	2	problems	problem	NOUN
ejpam-5895	80	3	can	can	AUX
ejpam-5895	80	4	be	be	AUX
ejpam-5895	80	5	quite	quite	ADV
ejpam-5895	80	6	challenging	challenging	ADJ
ejpam-5895	80	7	to	to	PART
ejpam-5895	80	8	solve	solve	VERB
ejpam-5895	80	9	due	due	ADP
ejpam-5895	80	10	to	to	ADP
ejpam-5895	80	11	their	their	PRON
ejpam-5895	80	12	intricate	intricate	ADJ
ejpam-5895	80	13	nature	nature	NOUN
ejpam-5895	80	14	.	.	PUNCT
ejpam-5895	81	1	traditional	traditional	ADJ
ejpam-5895	81	2	methods	method	NOUN
ejpam-5895	81	3	might	might	AUX
ejpam-5895	81	4	not	not	PART
ejpam-5895	81	5	always	always	ADV
ejpam-5895	81	6	be	be	AUX
ejpam-5895	81	7	sufficient	sufficient	ADJ
ejpam-5895	81	8	,	,	PUNCT
ejpam-5895	81	9	so	so	CCONJ
ejpam-5895	81	10	alternative	alternative	ADJ
ejpam-5895	81	11	methods	method	NOUN
ejpam-5895	81	12	are	be	AUX
ejpam-5895	81	13	often	often	ADV
ejpam-5895	81	14	employed	employ	VERB
ejpam-5895	81	15	to	to	PART
ejpam-5895	81	16	find	find	VERB
ejpam-5895	81	17	solutions	solution	NOUN
ejpam-5895	81	18	.	.	PUNCT
ejpam-5895	82	1	[	[	X
ejpam-5895	82	2	19–21	19–21	NUM
ejpam-5895	82	3	]	]	X
ejpam-5895	82	4	3	3	NUM
ejpam-5895	82	5	.	.	X
ejpam-5895	82	6	galerkin	galerkin	PROPN
ejpam-5895	82	7	finite	finite	PROPN
ejpam-5895	82	8	element	element	NOUN
ejpam-5895	82	9	method	method	NOUN
ejpam-5895	82	10	let	let	VERB
ejpam-5895	82	11	us	we	PRON
ejpam-5895	82	12	considered	consider	VERB
ejpam-5895	82	13	the	the	DET
ejpam-5895	82	14	model	model	NOUN
ejpam-5895	82	15	problem	problem	NOUN
ejpam-5895	82	16	:	:	PUNCT
ejpam-5895	82	17	poisson	poisson	NOUN
ejpam-5895	82	18	equation	equation	NOUN
ejpam-5895	82	19	with	with	ADP
ejpam-5895	82	20	homogenous	homogenous	ADJ
ejpam-5895	82	21	dirichlet	dirichlet	PROPN
ejpam-5895	82	22	boundary	boundary	ADJ
ejpam-5895	82	23	conditions	condition	NOUN
ejpam-5895	82	24	[	[	X
ejpam-5895	82	25	22	22	NUM
ejpam-5895	82	26	,	,	PUNCT
ejpam-5895	82	27	23	23	NUM
ejpam-5895	82	28	]	]	PUNCT
ejpam-5895	82	29	−∆u	−∆u	NOUN
ejpam-5895	83	1	=	=	SYM
ejpam-5895	83	2	f	f	PROPN
ejpam-5895	83	3	in	in	ADP
ejpam-5895	83	4	ω	ω	PROPN
ejpam-5895	83	5	(	(	PUNCT
ejpam-5895	83	6	2	2	NUM
ejpam-5895	83	7	)	)	PUNCT
ejpam-5895	83	8	u	u	NOUN
ejpam-5895	83	9	=	=	NOUN
ejpam-5895	83	10	0	0	NUM
ejpam-5895	83	11	on	on	ADP
ejpam-5895	83	12	∂ω	∂ω	PROPN
ejpam-5895	83	13	s.	s.	PROPN
ejpam-5895	83	14	s.	s.	PROPN
ejpam-5895	83	15	almutairi	almutairi	PROPN
ejpam-5895	83	16	,	,	PUNCT
ejpam-5895	83	17	a.	a.	PROPN
ejpam-5895	83	18	m.	m.	PROPN
ejpam-5895	83	19	saeed	saeed	PROPN
ejpam-5895	83	20	/	/	SYM
ejpam-5895	83	21	eur	eur	PROPN
ejpam-5895	83	22	.	.	PUNCT
ejpam-5895	84	1	j.	j.	PROPN
ejpam-5895	84	2	pure	pure	PROPN
ejpam-5895	84	3	appl	appl	PROPN
ejpam-5895	84	4	.	.	PROPN
ejpam-5895	84	5	math	math	PROPN
ejpam-5895	84	6	,	,	PUNCT
ejpam-5895	84	7	18	18	NUM
ejpam-5895	84	8	(	(	PUNCT
ejpam-5895	84	9	2	2	NUM
ejpam-5895	84	10	)	)	PUNCT
ejpam-5895	84	11	(	(	PUNCT
ejpam-5895	84	12	2025	2025	NUM
ejpam-5895	84	13	)	)	PUNCT
ejpam-5895	84	14	,	,	PUNCT
ejpam-5895	84	15	5895	5895	NUM
ejpam-5895	84	16	5	5	NUM
ejpam-5895	84	17	of	of	ADP
ejpam-5895	84	18	10	10	NUM
ejpam-5895	84	19	multiply	multiply	NOUN
ejpam-5895	84	20	a	a	DET
ejpam-5895	84	21	test	test	NOUN
ejpam-5895	84	22	function	function	NOUN
ejpam-5895	84	23	v	v	NOUN
ejpam-5895	84	24	,	,	PUNCT
ejpam-5895	84	25	integrate	integrate	VERB
ejpam-5895	84	26	over	over	ADP
ejpam-5895	84	27	ω	ω	NOUN
ejpam-5895	84	28	,	,	PUNCT
ejpam-5895	84	29	and	and	CCONJ
ejpam-5895	84	30	use	use	VERB
ejpam-5895	84	31	integration	integration	NOUN
ejpam-5895	84	32	by	by	ADP
ejpam-5895	84	33	parts	part	NOUN
ejpam-5895	84	34	to	to	PART
ejpam-5895	84	35	obtain	obtain	VERB
ejpam-5895	84	36	the	the	DET
ejpam-5895	84	37	corresponding	corresponding	ADJ
ejpam-5895	84	38	variational	variational	ADJ
ejpam-5895	84	39	formulation	formulation	NOUN
ejpam-5895	84	40	:	:	PUNCT
ejpam-5895	84	41	find	find	VERB
ejpam-5895	84	42	u	u	PRON
ejpam-5895	84	43	∈	∈	NOUN
ejpam-5895	84	44	v	v	NOUN
ejpam-5895	84	45	=	=	X
ejpam-5895	84	46	h1	h1	NOUN
ejpam-5895	84	47	0	0	NUM
ejpam-5895	84	48	(	(	PUNCT
ejpam-5895	84	49	ω	ω	NOUN
ejpam-5895	84	50	)	)	PUNCT
ejpam-5895	84	51	:	:	PUNCT
ejpam-5895	85	1	=	=	SYM
ejpam-5895	85	2	{	{	PUNCT
ejpam-5895	85	3	v	v	NUM
ejpam-5895	85	4	∈	∈	PROPN
ejpam-5895	85	5	l2(ω)|∇v	l2(ω)|∇v	PROPN
ejpam-5895	85	6	∈	∈	PROPN
ejpam-5895	85	7	l2(ω	l2(ω	PROPN
ejpam-5895	85	8	)	)	PUNCT
ejpam-5895	85	9	,	,	PUNCT
ejpam-5895	85	10	v|γ	v|γ	X
ejpam-5895	85	11	=	=	PUNCT
ejpam-5895	85	12	0	0	X
ejpam-5895	85	13	}	}	PUNCT
ejpam-5895	85	14	such	such	ADJ
ejpam-5895	85	15	that	that	SCONJ
ejpam-5895	85	16	a(u	a(u	PROPN
ejpam-5895	85	17	,	,	PUNCT
ejpam-5895	85	18	v	v	NOUN
ejpam-5895	85	19	)	)	PUNCT
ejpam-5895	85	20	=	=	SYM
ejpam-5895	85	21	(	(	PUNCT
ejpam-5895	85	22	f	f	X
ejpam-5895	85	23	,	,	PUNCT
ejpam-5895	85	24	v	v	NOUN
ejpam-5895	85	25	)	)	PUNCT
ejpam-5895	85	26	,	,	PUNCT
ejpam-5895	85	27	for	for	ADP
ejpam-5895	85	28	all	all	DET
ejpam-5895	85	29	v	v	ADP
ejpam-5895	85	30	∈	∈	PROPN
ejpam-5895	85	31	v	v	NOUN
ejpam-5895	85	32	,	,	PUNCT
ejpam-5895	85	33	(	(	PUNCT
ejpam-5895	85	34	3	3	X
ejpam-5895	85	35	)	)	PUNCT
ejpam-5895	85	36	where	where	SCONJ
ejpam-5895	85	37	a(u	a(u	PROPN
ejpam-5895	85	38	,	,	PUNCT
ejpam-5895	85	39	v	v	NOUN
ejpam-5895	85	40	)	)	PUNCT
ejpam-5895	85	41	=	=	SYM
ejpam-5895	86	1	∫	∫	PROPN
ejpam-5895	86	2	ω	ω	PROPN
ejpam-5895	86	3	∇u∇v	∇u∇v	NUM
ejpam-5895	86	4	dx	dx	PROPN
ejpam-5895	86	5	,	,	PUNCT
ejpam-5895	86	6	(	(	PUNCT
ejpam-5895	86	7	f	f	X
ejpam-5895	86	8	,	,	PUNCT
ejpam-5895	86	9	v	v	NOUN
ejpam-5895	86	10	)	)	PUNCT
ejpam-5895	86	11	=	=	SYM
ejpam-5895	87	1	∫	∫	PROPN
ejpam-5895	87	2	ω	ω	NUM
ejpam-5895	87	3	fv	fv	PROPN
ejpam-5895	87	4	dx	dx	PROPN
ejpam-5895	87	5	for	for	ADP
ejpam-5895	87	6	all	all	DET
ejpam-5895	87	7	f	f	PROPN
ejpam-5895	87	8	∈	∈	PROPN
ejpam-5895	87	9	l2(ω	l2(ω	PROPN
ejpam-5895	87	10	)	)	PUNCT
ejpam-5895	87	11	(	(	PUNCT
ejpam-5895	87	12	4	4	X
ejpam-5895	87	13	)	)	PUNCT
ejpam-5895	87	14	clearly	clearly	ADV
ejpam-5895	87	15	,	,	PUNCT
ejpam-5895	87	16	in	in	ADP
ejpam-5895	87	17	such	such	ADJ
ejpam-5895	87	18	case	case	NOUN
ejpam-5895	87	19	a	a	PRON
ejpam-5895	87	20	(	(	PUNCT
ejpam-5895	87	21	·	·	PUNCT
ejpam-5895	87	22	,	,	PUNCT
ejpam-5895	87	23	·	·	PUNCT
ejpam-5895	87	24	)	)	PUNCT
ejpam-5895	87	25	is	be	AUX
ejpam-5895	87	26	bilinear	bilinear	ADJ
ejpam-5895	87	27	and	and	CCONJ
ejpam-5895	87	28	symmetric	symmetric	ADJ
ejpam-5895	87	29	,	,	PUNCT
ejpam-5895	87	30	and	and	CCONJ
ejpam-5895	87	31	a(u	a(u	PROPN
ejpam-5895	87	32	,	,	PUNCT
ejpam-5895	87	33	u	u	NOUN
ejpam-5895	87	34	)	)	PUNCT
ejpam-5895	87	35	=	=	PUNCT
ejpam-5895	87	36	|u|21,ω	|u|21,ω	PUNCT
ejpam-5895	87	37	:	:	PUNCT
ejpam-5895	87	38	=	=	SYM
ejpam-5895	87	39	||u||2	||u||2	PROPN
ejpam-5895	87	40	furthermore	furthermore	ADV
ejpam-5895	87	41	a(u	a(u	PROPN
ejpam-5895	87	42	,	,	PUNCT
ejpam-5895	87	43	u	u	NOUN
ejpam-5895	87	44	)	)	PUNCT
ejpam-5895	87	45	=	=	SYM
ejpam-5895	87	46	0	0	NUM
ejpam-5895	87	47	implies	imply	VERB
ejpam-5895	87	48	∇u	∇u	PROPN
ejpam-5895	87	49	=	=	SYM
ejpam-5895	87	50	0	0	NUM
ejpam-5895	87	51	and	and	CCONJ
ejpam-5895	87	52	consequently	consequently	ADV
ejpam-5895	87	53	u	u	NOUN
ejpam-5895	87	54	is	be	AUX
ejpam-5895	87	55	constant	constant	ADJ
ejpam-5895	87	56	.	.	PUNCT
ejpam-5895	88	1	as	as	ADP
ejpam-5895	88	2	u|γ	u|γ	PROPN
ejpam-5895	88	3	=	=	SYM
ejpam-5895	88	4	0	0	PROPN
ejpam-5895	88	5	,	,	PUNCT
ejpam-5895	88	6	this	this	DET
ejpam-5895	88	7	constant	constant	ADJ
ejpam-5895	88	8	should	should	AUX
ejpam-5895	88	9	be	be	AUX
ejpam-5895	88	10	zero	zero	NUM
ejpam-5895	88	11	.	.	PUNCT
ejpam-5895	89	1	therefore	therefore	ADV
ejpam-5895	89	2	a	a	PRON
ejpam-5895	89	3	(	(	PUNCT
ejpam-5895	89	4	·	·	PUNCT
ejpam-5895	89	5	,	,	PUNCT
ejpam-5895	89	6	·	·	PUNCT
ejpam-5895	89	7	)	)	PUNCT
ejpam-5895	89	8	defines	define	VERB
ejpam-5895	89	9	an	an	DET
ejpam-5895	89	10	inner	inner	ADJ
ejpam-5895	89	11	product	product	NOUN
ejpam-5895	89	12	on	on	ADP
ejpam-5895	89	13	v	v	NUM
ejpam-5895	89	14	,	,	PUNCT
ejpam-5895	89	15	and	and	CCONJ
ejpam-5895	89	16	thus	thus	ADV
ejpam-5895	89	17	the	the	DET
ejpam-5895	89	18	problem	problem	NOUN
ejpam-5895	89	19	(	(	PUNCT
ejpam-5895	89	20	2	2	X
ejpam-5895	89	21	)	)	PUNCT
ejpam-5895	89	22	has	have	VERB
ejpam-5895	89	23	a	a	DET
ejpam-5895	89	24	unique	unique	ADJ
ejpam-5895	89	25	solution	solution	NOUN
ejpam-5895	89	26	by	by	ADP
ejpam-5895	89	27	the	the	DET
ejpam-5895	89	28	riesz	riesz	PROPN
ejpam-5895	89	29	representation	representation	NOUN
ejpam-5895	89	30	theorem	theorem	VERB
ejpam-5895	89	31	.	.	PUNCT
ejpam-5895	90	1	we	we	PRON
ejpam-5895	90	2	now	now	ADV
ejpam-5895	90	3	consider	consider	VERB
ejpam-5895	90	4	a	a	DET
ejpam-5895	90	5	class	class	NOUN
ejpam-5895	90	6	of	of	ADP
ejpam-5895	90	7	methods	method	NOUN
ejpam-5895	90	8	,	,	PUNCT
ejpam-5895	90	9	known	know	VERB
ejpam-5895	90	10	as	as	ADP
ejpam-5895	90	11	galerkin	galerkin	ADJ
ejpam-5895	90	12	methods	method	NOUN
ejpam-5895	90	13	which	which	PRON
ejpam-5895	90	14	are	be	AUX
ejpam-5895	90	15	used	use	VERB
ejpam-5895	90	16	to	to	PART
ejpam-5895	90	17	approximate	approximate	VERB
ejpam-5895	90	18	the	the	DET
ejpam-5895	90	19	solution	solution	NOUN
ejpam-5895	90	20	to	to	ADP
ejpam-5895	90	21	(	(	PUNCT
ejpam-5895	90	22	2	2	NUM
ejpam-5895	90	23	)	)	PUNCT
ejpam-5895	90	24	.	.	PUNCT
ejpam-5895	91	1	consider	consider	VERB
ejpam-5895	91	2	a	a	DET
ejpam-5895	91	3	finite	finite	ADJ
ejpam-5895	91	4	dimensional	dimensional	ADJ
ejpam-5895	91	5	subspace	subspace	NOUN
ejpam-5895	91	6	vh	vh	PROPN
ejpam-5895	91	7	⊂	⊂	PROPN
ejpam-5895	91	8	v	v	PROPN
ejpam-5895	91	9	.	.	PUNCT
ejpam-5895	92	1	restrict	restrict	VERB
ejpam-5895	92	2	the	the	DET
ejpam-5895	92	3	variational	variational	ADJ
ejpam-5895	92	4	form	form	NOUN
ejpam-5895	92	5	in	in	ADP
ejpam-5895	92	6	the	the	DET
ejpam-5895	92	7	subspace	subspace	NOUN
ejpam-5895	92	8	vh	vh	PROPN
ejpam-5895	92	9	,	,	PUNCT
ejpam-5895	92	10	i.e.	i.e.	ADV
ejpam-5895	92	11	,	,	PUNCT
ejpam-5895	92	12	find	find	VERB
ejpam-5895	92	13	uh	uh	INTJ
ejpam-5895	92	14	∈	∈	PROPN
ejpam-5895	92	15	v	v	PROPN
ejpam-5895	92	16	s.t	s.t	PROPN
ejpam-5895	92	17	.	.	PROPN
ejpam-5895	92	18	a(uh	a(uh	PROPN
ejpam-5895	92	19	,	,	PUNCT
ejpam-5895	92	20	vh	vh	PROPN
ejpam-5895	92	21	)	)	PUNCT
ejpam-5895	92	22	=	=	PUNCT
ejpam-5895	93	1	(	(	PUNCT
ejpam-5895	93	2	f	f	X
ejpam-5895	93	3	,	,	PUNCT
ejpam-5895	93	4	vh	vh	PROPN
ejpam-5895	93	5	)	)	PUNCT
ejpam-5895	93	6	,	,	PUNCT
ejpam-5895	93	7	for	for	ADP
ejpam-5895	93	8	all	all	DET
ejpam-5895	93	9	vh	vh	PROPN
ejpam-5895	93	10	∈	∈	PROPN
ejpam-5895	93	11	v	v	NOUN
ejpam-5895	93	12	(	(	PUNCT
ejpam-5895	93	13	5	5	NUM
ejpam-5895	93	14	)	)	PUNCT
ejpam-5895	93	15	let	let	VERB
ejpam-5895	93	16	vh	vh	PROPN
ejpam-5895	93	17	=	=	SYM
ejpam-5895	93	18	span{φ1	span{φ1	ADJ
ejpam-5895	93	19	,	,	PUNCT
ejpam-5895	93	20	φ2	φ2	PROPN
ejpam-5895	93	21	,	,	PUNCT
ejpam-5895	93	22	...	...	PUNCT
ejpam-5895	93	23	,	,	PUNCT
ejpam-5895	93	24	φn	φn	ADP
ejpam-5895	93	25	}	}	PUNCT
ejpam-5895	93	26	for	for	ADP
ejpam-5895	93	27	any	any	DET
ejpam-5895	93	28	function	function	NOUN
ejpam-5895	93	29	v	v	ADP
ejpam-5895	93	30	∈	∈	PROPN
ejpam-5895	93	31	vh	vh	NOUN
ejpam-5895	93	32	,	,	PUNCT
ejpam-5895	93	33	there	there	PRON
ejpam-5895	93	34	is	be	VERB
ejpam-5895	93	35	a	a	DET
ejpam-5895	93	36	unique	unique	ADJ
ejpam-5895	93	37	representation	representation	NOUN
ejpam-5895	93	38	:	:	PUNCT
ejpam-5895	94	1	v	v	NOUN
ejpam-5895	94	2	=	=	SYM
ejpam-5895	94	3	∑n	∑n	PROPN
ejpam-5895	94	4	i=1	i=1	PROPN
ejpam-5895	95	1	viφi	viφi	NOUN
ejpam-5895	95	2	we	we	PRON
ejpam-5895	95	3	thus	thus	ADV
ejpam-5895	95	4	can	can	AUX
ejpam-5895	95	5	define	define	VERB
ejpam-5895	95	6	an	an	DET
ejpam-5895	95	7	isomorphism	isomorphism	NOUN
ejpam-5895	95	8	vh	vh	PROPN
ejpam-5895	95	9	∼=	∼=	PROPN
ejpam-5895	95	10	rn	rn	PROPN
ejpam-5895	95	11	by	by	ADP
ejpam-5895	95	12	v	v	NOUN
ejpam-5895	95	13	=	=	SYM
ejpam-5895	95	14	n∑	n∑	PROPN
ejpam-5895	95	15	i=1	i=1	PROPN
ejpam-5895	95	16	viφi	viφi	NOUN
ejpam-5895	96	1	←→	←→	PROPN
ejpam-5895	96	2	v	v	NOUN
ejpam-5895	96	3	=	=	PUNCT
ejpam-5895	96	4	(	(	PUNCT
ejpam-5895	96	5	v1	v1	PROPN
ejpam-5895	96	6	,	,	PUNCT
ejpam-5895	96	7	...	...	PUNCT
ejpam-5895	96	8	,	,	PUNCT
ejpam-5895	96	9	vn	vn	PROPN
ejpam-5895	96	10	)	)	PUNCT
ejpam-5895	96	11	t	t	PROPN
ejpam-5895	96	12	,	,	PUNCT
ejpam-5895	96	13	and	and	CCONJ
ejpam-5895	96	14	call	call	VERB
ejpam-5895	96	15	v	v	ADP
ejpam-5895	96	16	the	the	DET
ejpam-5895	96	17	coordinate	coordinate	NOUN
ejpam-5895	96	18	vector	vector	NOUN
ejpam-5895	96	19	of	of	ADP
ejpam-5895	96	20	v	v	NOUN
ejpam-5895	96	21	relative	relative	ADJ
ejpam-5895	96	22	to	to	ADP
ejpam-5895	96	23	the	the	DET
ejpam-5895	96	24	basis	basis	NOUN
ejpam-5895	96	25	{	{	PUNCT
ejpam-5895	96	26	φ}ni=1	φ}ni=1	VERB
ejpam-5895	96	27	following	follow	VERB
ejpam-5895	96	28	the	the	DET
ejpam-5895	96	29	terminology	terminology	NOUN
ejpam-5895	96	30	in	in	ADP
ejpam-5895	96	31	elasticity	elasticity	NOUN
ejpam-5895	96	32	,	,	PUNCT
ejpam-5895	96	33	we	we	PRON
ejpam-5895	96	34	introduce	introduce	VERB
ejpam-5895	96	35	the	the	DET
ejpam-5895	96	36	stiffness	stiffness	ADJ
ejpam-5895	96	37	matrix	matrix	NOUN
ejpam-5895	96	38	a	a	DET
ejpam-5895	96	39	=	=	SYM
ejpam-5895	96	40	(	(	PUNCT
ejpam-5895	96	41	aij)n	aij)n	PROPN
ejpam-5895	96	42	x	x	SYM
ejpam-5895	96	43	n	n	X
ejpam-5895	96	44	with	with	ADP
ejpam-5895	96	45	aij	aij	PROPN
ejpam-5895	96	46	=	=	SYM
ejpam-5895	96	47	a(∅j	a(∅j	PROPN
ejpam-5895	96	48	,	,	PUNCT
ejpam-5895	96	49	∅i	∅i	ADJ
ejpam-5895	96	50	)	)	PUNCT
ejpam-5895	96	51	and	and	CCONJ
ejpam-5895	96	52	the	the	DET
ejpam-5895	96	53	load	load	NOUN
ejpam-5895	96	54	vector	vector	NOUN
ejpam-5895	96	55	f	f	PROPN
ejpam-5895	96	56	=	=	PUNCT
ejpam-5895	96	57	{	{	PUNCT
ejpam-5895	96	58	⟨f	⟨f	X
ejpam-5895	96	59	,	,	PUNCT
ejpam-5895	96	60	φ⟩}nk=1	φ⟩}nk=1	PROPN
ejpam-5895	96	61	∈	∈	PROPN
ejpam-5895	96	62	rn	rn	PROPN
ejpam-5895	96	63	then	then	ADV
ejpam-5895	96	64	the	the	DET
ejpam-5895	96	65	variational	variational	ADJ
ejpam-5895	96	66	problem	problem	NOUN
ejpam-5895	96	67	(	(	PUNCT
ejpam-5895	96	68	5	5	NUM
ejpam-5895	96	69	)	)	PUNCT
ejpam-5895	96	70	on	on	ADP
ejpam-5895	96	71	vh	vh	PROPN
ejpam-5895	96	72	can	can	AUX
ejpam-5895	96	73	be	be	AUX
ejpam-5895	96	74	formulated	formulate	VERB
ejpam-5895	96	75	as	as	ADP
ejpam-5895	96	76	the	the	DET
ejpam-5895	96	77	following	following	ADJ
ejpam-5895	96	78	linear	linear	ADJ
ejpam-5895	96	79	algebraic	algebraic	ADJ
ejpam-5895	96	80	system	system	NOUN
ejpam-5895	96	81	au	au	PUNCT
ejpam-5895	96	82	=	=	SYM
ejpam-5895	96	83	f	f	PROPN
ejpam-5895	96	84	by	by	ADP
ejpam-5895	96	85	definition	definition	NOUN
ejpam-5895	96	86	,	,	PUNCT
ejpam-5895	96	87	for	for	ADP
ejpam-5895	96	88	two	two	NUM
ejpam-5895	96	89	functions	function	NOUN
ejpam-5895	96	90	,	,	PUNCT
ejpam-5895	96	91	vu	vu	PROPN
ejpam-5895	96	92	∈	∈	PROPN
ejpam-5895	96	93	vh	vh	PROPN
ejpam-5895	96	94	,	,	PUNCT
ejpam-5895	96	95	their	their	PRON
ejpam-5895	96	96	a	a	DET
ejpam-5895	96	97	(	(	PUNCT
ejpam-5895	96	98	·	·	PUNCT
ejpam-5895	96	99	,	,	PUNCT
ejpam-5895	96	100	·	·	PUNCT
ejpam-5895	96	101	)	)	PUNCT
ejpam-5895	96	102	-inner	-inner	NOUN
ejpam-5895	96	103	product	product	NOUN
ejpam-5895	96	104	is	be	AUX
ejpam-5895	96	105	realized	realize	VERB
ejpam-5895	96	106	by	by	ADP
ejpam-5895	96	107	the	the	DET
ejpam-5895	96	108	matrix	matrix	NOUN
ejpam-5895	96	109	product	product	NOUN
ejpam-5895	96	110	a(uh	a(uh	PROPN
ejpam-5895	96	111	,	,	PUNCT
ejpam-5895	96	112	vh	vh	PROPN
ejpam-5895	96	113	)	)	PUNCT
ejpam-5895	96	114	=	=	SYM
ejpam-5895	97	1	a	a	PRON
ejpam-5895	97	2	(	(	PUNCT
ejpam-5895	97	3	∑	∑	PROPN
ejpam-5895	97	4	i	i	PRON
ejpam-5895	97	5	uiφi	uiφi	PRON
ejpam-5895	97	6	,	,	PUNCT
ejpam-5895	97	7	∑	∑	ADV
ejpam-5895	97	8	vjφj	vjφj	ADJ
ejpam-5895	97	9	)	)	PUNCT
ejpam-5895	97	10	=	=	PUNCT
ejpam-5895	98	1	∑	∑	PUNCT
ejpam-5895	98	2	i	i	PROPN
ejpam-5895	98	3	,	,	PUNCT
ejpam-5895	98	4	j	j	PROPN
ejpam-5895	98	5	a(φi	a(φi	PROPN
ejpam-5895	98	6	,	,	PUNCT
ejpam-5895	98	7	φj)uivj	φj)uivj	NOUN
ejpam-5895	98	8	=	=	PUNCT
ejpam-5895	98	9	vtau	vtau	ADV
ejpam-5895	98	10	therefore	therefore	ADV
ejpam-5895	98	11	for	for	ADP
ejpam-5895	98	12	any	any	DET
ejpam-5895	98	13	vector	vector	NOUN
ejpam-5895	98	14	u	u	PROPN
ejpam-5895	98	15	∈	∈	PROPN
ejpam-5895	98	16	rn	rn	PROPN
ejpam-5895	98	17	,	,	PUNCT
ejpam-5895	98	18	utau	utau	PROPN
ejpam-5895	98	19	=	=	SYM
ejpam-5895	98	20	a(u	a(u	PROPN
ejpam-5895	98	21	,	,	PUNCT
ejpam-5895	98	22	u	u	NOUN
ejpam-5895	98	23	)	)	PUNCT
ejpam-5895	98	24	≥	≥	NOUN
ejpam-5895	98	25	0	0	NUM
ejpam-5895	98	26	and	and	CCONJ
ejpam-5895	98	27	equals	equal	VERB
ejpam-5895	98	28	0	0	PUNCT
ejpam-5895	99	1	if	if	SCONJ
ejpam-5895	99	2	and	and	CCONJ
ejpam-5895	99	3	only	only	ADV
ejpam-5895	99	4	if	if	SCONJ
ejpam-5895	99	5	u	u	NOUN
ejpam-5895	99	6	is	be	AUX
ejpam-5895	99	7	zero	zero	NUM
ejpam-5895	99	8	.	.	PUNCT
ejpam-5895	100	1	namely	namely	ADV
ejpam-5895	100	2	a	a	PRON
ejpam-5895	100	3	is	be	AUX
ejpam-5895	100	4	a	a	DET
ejpam-5895	100	5	symmetric	symmetric	ADJ
ejpam-5895	100	6	positive	positive	ADJ
ejpam-5895	100	7	definite	definite	ADJ
ejpam-5895	100	8	(	(	PUNCT
ejpam-5895	100	9	spd	spd	NOUN
ejpam-5895	100	10	)	)	PUNCT
ejpam-5895	100	11	matrix	matrix	NOUN
ejpam-5895	100	12	and	and	CCONJ
ejpam-5895	100	13	thus	thus	ADV
ejpam-5895	100	14	the	the	DET
ejpam-5895	100	15	solution	solution	NOUN
ejpam-5895	100	16	u	u	X
ejpam-5895	100	17	=	=	PUNCT
ejpam-5895	100	18	a−1f	a−1f	PROPN
ejpam-5895	100	19	exists	exist	VERB
ejpam-5895	100	20	and	and	CCONJ
ejpam-5895	100	21	unique	unique	ADJ
ejpam-5895	100	22	.	.	PUNCT
ejpam-5895	101	1	after	after	SCONJ
ejpam-5895	101	2	we	we	PRON
ejpam-5895	101	3	get	get	VERB
ejpam-5895	101	4	the	the	DET
ejpam-5895	101	5	coefficient	coefficient	NOUN
ejpam-5895	101	6	vector	vector	NOUN
ejpam-5895	101	7	u	u	PROPN
ejpam-5895	101	8	,	,	PUNCT
ejpam-5895	101	9	uh	uh	INTJ
ejpam-5895	101	10	can	can	AUX
ejpam-5895	101	11	be	be	AUX
ejpam-5895	101	12	obtained	obtain	VERB
ejpam-5895	101	13	by	by	ADP
ejpam-5895	101	14	linear	linear	ADJ
ejpam-5895	101	15	combination	combination	NOUN
ejpam-5895	101	16	of	of	ADP
ejpam-5895	101	17	basis	basis	NOUN
ejpam-5895	101	18	functions	function	NOUN
ejpam-5895	101	19	.	.	PUNCT
ejpam-5895	102	1	the	the	DET
ejpam-5895	102	2	finite	finite	PROPN
ejpam-5895	102	3	element	element	NOUN
ejpam-5895	102	4	method	method	NOUN
ejpam-5895	102	5	,	,	PUNCT
ejpam-5895	102	6	a	a	DET
ejpam-5895	102	7	prominent	prominent	ADJ
ejpam-5895	102	8	and	and	CCONJ
ejpam-5895	102	9	widely	widely	ADV
ejpam-5895	102	10	-	-	PUNCT
ejpam-5895	102	11	used	use	VERB
ejpam-5895	102	12	s.	s.	PROPN
ejpam-5895	102	13	s.	s.	PROPN
ejpam-5895	102	14	almutairi	almutairi	PROPN
ejpam-5895	102	15	,	,	PUNCT
ejpam-5895	102	16	a.	a.	PROPN
ejpam-5895	102	17	m.	m.	PROPN
ejpam-5895	102	18	saeed	saeed	PROPN
ejpam-5895	102	19	/	/	SYM
ejpam-5895	102	20	eur	eur	PROPN
ejpam-5895	102	21	.	.	PUNCT
ejpam-5895	103	1	j.	j.	PROPN
ejpam-5895	103	2	pure	pure	PROPN
ejpam-5895	103	3	appl	appl	PROPN
ejpam-5895	103	4	.	.	PROPN
ejpam-5895	103	5	math	math	PROPN
ejpam-5895	103	6	,	,	PUNCT
ejpam-5895	103	7	18	18	NUM
ejpam-5895	103	8	(	(	PUNCT
ejpam-5895	103	9	2	2	NUM
ejpam-5895	103	10	)	)	PUNCT
ejpam-5895	103	11	(	(	PUNCT
ejpam-5895	103	12	2025	2025	NUM
ejpam-5895	103	13	)	)	PUNCT
ejpam-5895	103	14	,	,	PUNCT
ejpam-5895	103	15	5895	5895	NUM
ejpam-5895	103	16	6	6	NUM
ejpam-5895	103	17	of	of	ADP
ejpam-5895	103	18	10	10	NUM
ejpam-5895	103	19	example	example	NOUN
ejpam-5895	103	20	of	of	ADP
ejpam-5895	103	21	galerkin	galerkin	ADJ
ejpam-5895	103	22	methods	method	NOUN
ejpam-5895	103	23	,	,	PUNCT
ejpam-5895	103	24	constructs	construct	VERB
ejpam-5895	103	25	a	a	DET
ejpam-5895	103	26	finite	finite	ADJ
ejpam-5895	103	27	-	-	ADJ
ejpam-5895	103	28	dimensional	dimensional	ADJ
ejpam-5895	103	29	subspace	subspace	NOUN
ejpam-5895	103	30	vh	vh	NOUN
ejpam-5895	103	31	based	base	VERB
ejpam-5895	103	32	on	on	ADP
ejpam-5895	103	33	triangulations	triangulation	NOUN
ejpam-5895	103	34	τh	τh	ADP
ejpam-5895	103	35	of	of	ADP
ejpam-5895	103	36	the	the	DET
ejpam-5895	103	37	domain	domain	NOUN
ejpam-5895	103	38	.	.	PUNCT
ejpam-5895	104	1	the	the	DET
ejpam-5895	104	2	name	name	NOUN
ejpam-5895	104	3	comes	come	VERB
ejpam-5895	104	4	from	from	ADP
ejpam-5895	104	5	the	the	DET
ejpam-5895	104	6	fact	fact	NOUN
ejpam-5895	104	7	that	that	SCONJ
ejpam-5895	104	8	the	the	DET
ejpam-5895	104	9	domain	domain	NOUN
ejpam-5895	104	10	is	be	AUX
ejpam-5895	104	11	decomposed	decompose	VERB
ejpam-5895	104	12	into	into	ADP
ejpam-5895	104	13	finite	finite	ADJ
ejpam-5895	104	14	number	number	NOUN
ejpam-5895	104	15	of	of	ADP
ejpam-5895	104	16	elements	element	NOUN
ejpam-5895	104	17	.	.	PUNCT
ejpam-5895	105	1	usually	usually	ADV
ejpam-5895	105	2	piecewise	piecewise	NOUN
ejpam-5895	105	3	polynomials	polynomial	NOUN
ejpam-5895	105	4	are	be	AUX
ejpam-5895	105	5	used	use	VERB
ejpam-5895	105	6	to	to	PART
ejpam-5895	105	7	define	define	VERB
ejpam-5895	105	8	a	a	DET
ejpam-5895	105	9	finite	finite	ADJ
ejpam-5895	105	10	dimensional	dimensional	ADJ
ejpam-5895	105	11	space	space	NOUN
ejpam-5895	105	12	.	.	PUNCT
ejpam-5895	106	1	4	4	X
ejpam-5895	106	2	.	.	NOUN
ejpam-5895	106	3	numerical	numerical	ADJ
ejpam-5895	106	4	experiments	experiment	NOUN
ejpam-5895	106	5	consider	consider	VERB
ejpam-5895	106	6	poisson	poisson	NOUN
ejpam-5895	106	7	equation	equation	NOUN
ejpam-5895	106	8	∂2u	∂2u	PROPN
ejpam-5895	106	9	∂x2	∂x2	PROPN
ejpam-5895	106	10	+	+	CCONJ
ejpam-5895	106	11	∂2u	∂2u	ADJ
ejpam-5895	106	12	∂y2	∂y2	NOUN
ejpam-5895	107	1	=	=	PUNCT
ejpam-5895	107	2	xy	xy	PROPN
ejpam-5895	107	3	(	(	PUNCT
ejpam-5895	107	4	6	6	NUM
ejpam-5895	107	5	)	)	PUNCT
ejpam-5895	107	6	subject	subject	NOUN
ejpam-5895	107	7	to	to	ADP
ejpam-5895	107	8	the	the	DET
ejpam-5895	107	9	boundary	boundary	ADJ
ejpam-5895	107	10	conditions	condition	NOUN
ejpam-5895	107	11	u(x	u(x	NOUN
ejpam-5895	107	12	,	,	PUNCT
ejpam-5895	107	13	0	0	NUM
ejpam-5895	107	14	)	)	PUNCT
ejpam-5895	107	15	=	=	SYM
ejpam-5895	107	16	0	0	NUM
ejpam-5895	107	17	,	,	PUNCT
ejpam-5895	107	18	u(x	u(x	NOUN
ejpam-5895	107	19	,	,	PUNCT
ejpam-5895	107	20	2	2	NUM
ejpam-5895	107	21	)	)	PUNCT
ejpam-5895	107	22	=	=	SYM
ejpam-5895	107	23	0	0	NUM
ejpam-5895	107	24	,	,	PUNCT
ejpam-5895	107	25	u(0	u(0	PROPN
ejpam-5895	107	26	,	,	PUNCT
ejpam-5895	107	27	y	y	PROPN
ejpam-5895	107	28	)	)	PUNCT
ejpam-5895	107	29	=	=	SYM
ejpam-5895	107	30	0	0	NUM
ejpam-5895	107	31	,	,	PUNCT
ejpam-5895	107	32	u(2	u(2	PROPN
ejpam-5895	107	33	,	,	PUNCT
ejpam-5895	107	34	y	y	PROPN
ejpam-5895	107	35	)	)	PUNCT
ejpam-5895	107	36	=	=	SYM
ejpam-5895	108	1	0	0	X
ejpam-5895	108	2	.	.	PUNCT
ejpam-5895	109	1	the	the	DET
ejpam-5895	109	2	analytical	analytical	ADJ
ejpam-5895	109	3	solution	solution	NOUN
ejpam-5895	109	4	of	of	ADP
ejpam-5895	109	5	the	the	DET
ejpam-5895	109	6	pde	pde	NOUN
ejpam-5895	109	7	is	be	AUX
ejpam-5895	109	8	u	u	NOUN
ejpam-5895	109	9	=	=	PUNCT
ejpam-5895	109	10	∑	∑	PUNCT
ejpam-5895	109	11	m≥1	m≥1	PROPN
ejpam-5895	109	12	∑	∑	PUNCT
ejpam-5895	109	13	n≥1	n≥1	VERB
ejpam-5895	109	14	−16	−16	PROPN
ejpam-5895	109	15	π2	π2	NOUN
ejpam-5895	109	16	(	(	PUNCT
ejpam-5895	109	17	−1)n+m	−1)n+m	PROPN
ejpam-5895	109	18	nmλnm	nmλnm	ADJ
ejpam-5895	109	19	sin	sin	NOUN
ejpam-5895	109	20	(	(	PUNCT
ejpam-5895	109	21	nπx	nπx	NOUN
ejpam-5895	109	22	2	2	NUM
ejpam-5895	109	23	)	)	PUNCT
ejpam-5895	109	24	sin	sin	NOUN
ejpam-5895	109	25	(	(	PUNCT
ejpam-5895	109	26	mπy	mπy	NOUN
ejpam-5895	109	27	2	2	NUM
ejpam-5895	109	28	)	)	PUNCT
ejpam-5895	109	29	(	(	PUNCT
ejpam-5895	109	30	7	7	X
ejpam-5895	109	31	)	)	PUNCT
ejpam-5895	109	32	table	table	NOUN
ejpam-5895	109	33	1	1	NUM
ejpam-5895	109	34	shows	show	VERB
ejpam-5895	109	35	the	the	DET
ejpam-5895	109	36	approximations	approximation	NOUN
ejpam-5895	109	37	solutions	solution	NOUN
ejpam-5895	109	38	of	of	ADP
ejpam-5895	109	39	gfem	gfem	NOUN
ejpam-5895	109	40	and	and	CCONJ
ejpam-5895	109	41	fdm	fdm	VERB
ejpam-5895	109	42	with	with	ADP
ejpam-5895	109	43	the	the	DET
ejpam-5895	109	44	analytical	analytical	ADJ
ejpam-5895	109	45	solution	solution	NOUN
ejpam-5895	109	46	of	of	ADP
ejpam-5895	109	47	the	the	DET
ejpam-5895	109	48	proposed	propose	VERB
ejpam-5895	109	49	problem	problem	NOUN
ejpam-5895	109	50	.	.	PUNCT
ejpam-5895	110	1	the	the	DET
ejpam-5895	110	2	results	result	NOUN
ejpam-5895	110	3	reveal	reveal	VERB
ejpam-5895	110	4	that	that	SCONJ
ejpam-5895	110	5	gfem	gfem	PROPN
ejpam-5895	110	6	works	work	NOUN
ejpam-5895	110	7	will	will	AUX
ejpam-5895	110	8	better	well	ADV
ejpam-5895	110	9	than	than	ADP
ejpam-5895	110	10	fdm	fdm	NOUN
ejpam-5895	110	11	because	because	SCONJ
ejpam-5895	110	12	the	the	DET
ejpam-5895	110	13	approximation	approximation	NOUN
ejpam-5895	110	14	solutions	solution	NOUN
ejpam-5895	110	15	resulted	result	VERB
ejpam-5895	110	16	from	from	ADP
ejpam-5895	110	17	gfem	gfem	VERB
ejpam-5895	110	18	close	close	ADV
ejpam-5895	110	19	to	to	ADP
ejpam-5895	110	20	the	the	DET
ejpam-5895	110	21	analytical	analytical	ADJ
ejpam-5895	110	22	solutions	solution	NOUN
ejpam-5895	110	23	.	.	PUNCT
ejpam-5895	111	1	table	table	NOUN
ejpam-5895	111	2	1	1	NUM
ejpam-5895	111	3	:	:	PUNCT
ejpam-5895	111	4	comparison	comparison	NOUN
ejpam-5895	111	5	results	result	NOUN
ejpam-5895	111	6	of	of	ADP
ejpam-5895	111	7	the	the	DET
ejpam-5895	111	8	approximation	approximation	NOUN
ejpam-5895	111	9	solutions	solution	NOUN
ejpam-5895	111	10	from	from	ADP
ejpam-5895	111	11	fdm	fdm	NOUN
ejpam-5895	111	12	,	,	PUNCT
ejpam-5895	111	13	gfem	gfem	PROPN
ejpam-5895	111	14	and	and	CCONJ
ejpam-5895	111	15	the	the	DET
ejpam-5895	111	16	analytical	analytical	ADJ
ejpam-5895	111	17	solution	solution	NOUN
ejpam-5895	111	18	of	of	ADP
ejpam-5895	111	19	the	the	DET
ejpam-5895	111	20	proposed	propose	VERB
ejpam-5895	111	21	problem	problem	NOUN
ejpam-5895	111	22	.	.	PUNCT
ejpam-5895	112	1	nodes	node	NOUN
ejpam-5895	112	2	fdm	fdm	VERB
ejpam-5895	112	3	gfem	gfem	ADJ
ejpam-5895	112	4	analytical	analytical	ADJ
ejpam-5895	112	5	solution	solution	NOUN
ejpam-5895	112	6	1	1	NUM
ejpam-5895	112	7	0	0	NUM
ejpam-5895	112	8	0	0	NUM
ejpam-5895	112	9	0	0	NUM
ejpam-5895	112	10	2	2	NUM
ejpam-5895	112	11	−0.119349193976091	−0.119349193976091	NOUN
ejpam-5895	112	12	−0.122668821548822	−0.122668821548822	NOUN
ejpam-5895	112	13	−0.1226832533	−0.1226832533	X
ejpam-5895	112	14	3	3	NUM
ejpam-5895	112	15	−0.11477288471148	−0.11477288471148	NOUN
ejpam-5895	112	16	−0.117143703703704	−0.117143703703704	NUM
ejpam-5895	112	17	−0.1176222268	−0.1176222268	NUM
ejpam-5895	112	18	4	4	NUM
ejpam-5895	112	19	−0.119349193976091	−0.119349193976091	NOUN
ejpam-5895	112	20	−0.122668821548822	−0.122668821548822	NOUN
ejpam-5895	112	21	−0.1226832533	−0.1226832533	X
ejpam-5895	112	22	5	5	NUM
ejpam-5895	112	23	−0.216687033077673	−0.216687033077673	NOUN
ejpam-5895	112	24	−0.221429225589226	−0.221429225589226	NOUN
ejpam-5895	112	25	−0.222990496	−0.222990496	NOUN
ejpam-5895	112	26	6	6	NUM
ejpam-5895	112	27	−0.213255170322128	−0.213255170322128	NOUN
ejpam-5895	112	28	−0.216574276094276	−0.216574276094276	X
ejpam-5895	112	29	−0.2194532299	−0.2194532299	NOUN
ejpam-5895	112	30	7	7	NUM
ejpam-5895	112	31	−0.262825492159407	−0.262825492159407	NUM
ejpam-5895	112	32	−0.267567407407407	−0.267567407407407	NOUN
ejpam-5895	112	33	−0.2707333253	−0.2707333253	NUM
ejpam-5895	112	34	table	table	NOUN
ejpam-5895	112	35	2	2	NUM
ejpam-5895	112	36	:	:	PUNCT
ejpam-5895	112	37	absolute	absolute	ADJ
ejpam-5895	112	38	errors	error	NOUN
ejpam-5895	112	39	of	of	ADP
ejpam-5895	112	40	the	the	DET
ejpam-5895	112	41	fdm	fdm	NOUN
ejpam-5895	112	42	for	for	ADP
ejpam-5895	112	43	solving	solve	VERB
ejpam-5895	112	44	the	the	DET
ejpam-5895	112	45	proposed	propose	VERB
ejpam-5895	112	46	problem	problem	NOUN
ejpam-5895	112	47	.	.	PUNCT
ejpam-5895	113	1	nodes	nod	VERB
ejpam-5895	113	2	fdm	fdm	VERB
ejpam-5895	113	3	analytical	analytical	ADJ
ejpam-5895	113	4	solution	solution	NOUN
ejpam-5895	113	5	absolute	absolute	ADJ
ejpam-5895	113	6	error	error	NOUN
ejpam-5895	113	7	1	1	NUM
ejpam-5895	113	8	0	0	NUM
ejpam-5895	113	9	0	0	NUM
ejpam-5895	113	10	0	0	NUM
ejpam-5895	113	11	2	2	NUM
ejpam-5895	113	12	−0.119349193976091	−0.119349193976091	NOUN
ejpam-5895	113	13	−0.1226832533	−0.1226832533	X
ejpam-5895	113	14	0.003334059324	0.003334059324	NUM
ejpam-5895	113	15	3	3	NUM
ejpam-5895	113	16	−0.11477288471148	−0.11477288471148	NOUN
ejpam-5895	113	17	−0.1176222268	−0.1176222268	NUM
ejpam-5895	113	18	0.002849342089	0.002849342089	NUM
ejpam-5895	113	19	4	4	NUM
ejpam-5895	113	20	−0.119349193976091	−0.119349193976091	NOUN
ejpam-5895	113	21	−0.1226832533	−0.1226832533	X
ejpam-5895	113	22	0.003334059324	0.003334059324	NUM
ejpam-5895	113	23	5	5	NUM
ejpam-5895	113	24	−0.216687033077673	−0.216687033077673	NOUN
ejpam-5895	113	25	-0.222990496	-0.222990496	NOUN
ejpam-5895	113	26	0.006303462922	0.006303462922	NUM
ejpam-5895	113	27	6	6	NUM
ejpam-5895	113	28	−0.213255170322128	−0.213255170322128	NOUN
ejpam-5895	113	29	−0.2194532299	−0.2194532299	NOUN
ejpam-5895	113	30	0.006198059578	0.006198059578	NUM
ejpam-5895	113	31	7	7	NUM
ejpam-5895	113	32	−0.262825492159407	−0.262825492159407	NOUN
ejpam-5895	113	33	−0.2707333253	−0.2707333253	PROPN
ejpam-5895	114	1	0.007907833141	0.007907833141	NUM
ejpam-5895	114	2	s.	s.	PROPN
ejpam-5895	114	3	s.	s.	PROPN
ejpam-5895	114	4	almutairi	almutairi	PROPN
ejpam-5895	114	5	,	,	PUNCT
ejpam-5895	114	6	a.	a.	PROPN
ejpam-5895	114	7	m.	m.	PROPN
ejpam-5895	114	8	saeed	saeed	PROPN
ejpam-5895	114	9	/	/	SYM
ejpam-5895	114	10	eur	eur	PROPN
ejpam-5895	114	11	.	.	PUNCT
ejpam-5895	115	1	j.	j.	PROPN
ejpam-5895	115	2	pure	pure	PROPN
ejpam-5895	115	3	appl	appl	PROPN
ejpam-5895	115	4	.	.	PROPN
ejpam-5895	115	5	math	math	PROPN
ejpam-5895	115	6	,	,	PUNCT
ejpam-5895	115	7	18	18	NUM
ejpam-5895	115	8	(	(	PUNCT
ejpam-5895	115	9	2	2	NUM
ejpam-5895	115	10	)	)	PUNCT
ejpam-5895	115	11	(	(	PUNCT
ejpam-5895	115	12	2025	2025	NUM
ejpam-5895	115	13	)	)	PUNCT
ejpam-5895	115	14	,	,	PUNCT
ejpam-5895	115	15	5895	5895	NUM
ejpam-5895	115	16	7	7	NUM
ejpam-5895	115	17	of	of	ADP
ejpam-5895	115	18	10	10	NUM
ejpam-5895	115	19	table	table	NOUN
ejpam-5895	115	20	3	3	NUM
ejpam-5895	115	21	:	:	PUNCT
ejpam-5895	115	22	absolute	absolute	ADJ
ejpam-5895	115	23	errors	error	NOUN
ejpam-5895	115	24	of	of	ADP
ejpam-5895	115	25	the	the	DET
ejpam-5895	115	26	gfem	gfem	NOUN
ejpam-5895	115	27	for	for	ADP
ejpam-5895	115	28	solving	solve	VERB
ejpam-5895	115	29	the	the	DET
ejpam-5895	115	30	proposed	propose	VERB
ejpam-5895	115	31	problem	problem	NOUN
ejpam-5895	115	32	.	.	PUNCT
ejpam-5895	116	1	nodes	node	NOUN
ejpam-5895	116	2	gfem	gfem	VERB
ejpam-5895	116	3	analytical	analytical	ADJ
ejpam-5895	116	4	solution	solution	NOUN
ejpam-5895	116	5	absolute	absolute	ADJ
ejpam-5895	116	6	error	error	NOUN
ejpam-5895	116	7	1	1	NUM
ejpam-5895	116	8	0	0	NUM
ejpam-5895	116	9	0	0	NUM
ejpam-5895	116	10	0	0	NUM
ejpam-5895	116	11	2	2	NUM
ejpam-5895	116	12	−0.122668821548822	−0.122668821548822	NOUN
ejpam-5895	116	13	−0.1226832533	−0.1226832533	X
ejpam-5895	117	1	−0.00001443175118	−0.00001443175118	NOUN
ejpam-5895	117	2	3	3	NUM
ejpam-5895	117	3	−0.117143703703704	−0.117143703703704	NUM
ejpam-5895	117	4	−0.1176222268	−0.1176222268	PROPN
ejpam-5895	117	5	−0.0004785230963	−0.0004785230963	NUM
ejpam-5895	117	6	4	4	NUM
ejpam-5895	117	7	−0.122668821548822	−0.122668821548822	NOUN
ejpam-5895	117	8	−0.1226832533	−0.1226832533	X
ejpam-5895	118	1	−0.00001443175118	−0.00001443175118	NOUN
ejpam-5895	118	2	5	5	NUM
ejpam-5895	118	3	−0.221429225589226	−0.221429225589226	NOUN
ejpam-5895	118	4	−0.222990496	−0.222990496	NOUN
ejpam-5895	118	5	−0.001561270411	−0.001561270411	PUNCT
ejpam-5895	118	6	6	6	NUM
ejpam-5895	118	7	−0.216574276094276	−0.216574276094276	X
ejpam-5895	118	8	−0.2194532299	−0.2194532299	X
ejpam-5895	118	9	−0.002878953806	−0.002878953806	X
ejpam-5895	118	10	7	7	NUM
ejpam-5895	118	11	−0.267567407407407	−0.267567407407407	NOUN
ejpam-5895	118	12	−0.2707333253	−0.2707333253	PUNCT
ejpam-5895	118	13	−0.003165917893	−0.003165917893	NOUN
ejpam-5895	118	14	tables	table	NOUN
ejpam-5895	118	15	2	2	NUM
ejpam-5895	118	16	and	and	CCONJ
ejpam-5895	118	17	3	3	NUM
ejpam-5895	118	18	show	show	VERB
ejpam-5895	118	19	the	the	DET
ejpam-5895	118	20	absolute	absolute	ADJ
ejpam-5895	118	21	error	error	NOUN
ejpam-5895	118	22	in	in	ADP
ejpam-5895	118	23	the	the	DET
ejpam-5895	118	24	case	case	NOUN
ejpam-5895	118	25	of	of	ADP
ejpam-5895	118	26	fdm	fdm	NOUN
ejpam-5895	118	27	and	and	CCONJ
ejpam-5895	118	28	gfem	gfem	NOUN
ejpam-5895	118	29	.	.	PUNCT
ejpam-5895	119	1	we	we	PRON
ejpam-5895	119	2	can	can	AUX
ejpam-5895	119	3	observe	observe	VERB
ejpam-5895	119	4	that	that	SCONJ
ejpam-5895	119	5	the	the	DET
ejpam-5895	119	6	absolute	absolute	ADJ
ejpam-5895	119	7	errors	error	NOUN
ejpam-5895	119	8	of	of	ADP
ejpam-5895	119	9	gfem	gfem	NOUN
ejpam-5895	119	10	smaller	small	ADJ
ejpam-5895	119	11	than	than	ADP
ejpam-5895	119	12	fdm	fdm	NOUN
ejpam-5895	119	13	which	which	PRON
ejpam-5895	119	14	implies	imply	VERB
ejpam-5895	119	15	that	that	SCONJ
ejpam-5895	119	16	the	the	DET
ejpam-5895	119	17	gfem	gfem	NOUN
ejpam-5895	119	18	has	have	VERB
ejpam-5895	119	19	more	more	ADJ
ejpam-5895	119	20	accuracy	accuracy	NOUN
ejpam-5895	119	21	than	than	ADP
ejpam-5895	119	22	fdm	fdm	NOUN
ejpam-5895	119	23	.	.	PUNCT
ejpam-5895	120	1	figure	figure	NOUN
ejpam-5895	120	2	2	2	NUM
ejpam-5895	120	3	:	:	PUNCT
ejpam-5895	120	4	comparison	comparison	NOUN
ejpam-5895	120	5	between	between	ADP
ejpam-5895	120	6	the	the	DET
ejpam-5895	120	7	approximation	approximation	NOUN
ejpam-5895	120	8	solution	solution	NOUN
ejpam-5895	120	9	by	by	ADP
ejpam-5895	120	10	fdm	fdm	NOUN
ejpam-5895	120	11	and	and	CCONJ
ejpam-5895	120	12	analytical	analytical	ADJ
ejpam-5895	120	13	solution	solution	NOUN
ejpam-5895	120	14	.	.	PUNCT
ejpam-5895	121	1	figure	figure	VERB
ejpam-5895	121	2	3	3	NUM
ejpam-5895	121	3	:	:	PUNCT
ejpam-5895	121	4	comparison	comparison	NOUN
ejpam-5895	121	5	between	between	ADP
ejpam-5895	121	6	the	the	DET
ejpam-5895	121	7	approximation	approximation	NOUN
ejpam-5895	121	8	solution	solution	NOUN
ejpam-5895	121	9	by	by	ADP
ejpam-5895	121	10	gfem	gfem	PROPN
ejpam-5895	121	11	and	and	CCONJ
ejpam-5895	121	12	analytical	analytical	ADJ
ejpam-5895	121	13	solution	solution	NOUN
ejpam-5895	121	14	.	.	PUNCT
ejpam-5895	122	1	from	from	ADP
ejpam-5895	122	2	figures	figure	NOUN
ejpam-5895	122	3	2	2	NUM
ejpam-5895	122	4	and	and	CCONJ
ejpam-5895	122	5	3	3	NUM
ejpam-5895	122	6	we	we	PRON
ejpam-5895	122	7	can	can	AUX
ejpam-5895	122	8	observe	observe	VERB
ejpam-5895	122	9	that	that	SCONJ
ejpam-5895	122	10	the	the	DET
ejpam-5895	122	11	error	error	NOUN
ejpam-5895	122	12	associated	associate	VERB
ejpam-5895	122	13	with	with	ADP
ejpam-5895	122	14	the	the	DET
ejpam-5895	122	15	fdm	fdm	NOUN
ejpam-5895	122	16	is	be	AUX
ejpam-5895	122	17	higher	high	ADJ
ejpam-5895	122	18	compared	compare	VERB
ejpam-5895	122	19	to	to	ADP
ejpam-5895	122	20	that	that	PRON
ejpam-5895	122	21	of	of	ADP
ejpam-5895	122	22	the	the	DET
ejpam-5895	122	23	gfem	gfem	NOUN
ejpam-5895	122	24	.	.	PUNCT
ejpam-5895	123	1	figures	figure	VERB
ejpam-5895	123	2	4,5	4,5	NUM
ejpam-5895	123	3	and	and	CCONJ
ejpam-5895	123	4	6	6	NUM
ejpam-5895	123	5	show	show	VERB
ejpam-5895	123	6	clearly	clearly	ADV
ejpam-5895	123	7	the	the	DET
ejpam-5895	123	8	absolute	absolute	ADJ
ejpam-5895	123	9	errors	error	NOUN
ejpam-5895	123	10	of	of	ADP
ejpam-5895	123	11	fdm	fdm	NOUN
ejpam-5895	123	12	and	and	CCONJ
ejpam-5895	123	13	gfem	gfem	VERB
ejpam-5895	123	14	with	with	ADP
ejpam-5895	123	15	the	the	DET
ejpam-5895	123	16	analytical	analytical	ADJ
ejpam-5895	123	17	solution	solution	NOUN
ejpam-5895	123	18	and	and	CCONJ
ejpam-5895	123	19	it	it	PRON
ejpam-5895	123	20	is	be	AUX
ejpam-5895	123	21	noticeable	noticeable	ADJ
ejpam-5895	123	22	that	that	SCONJ
ejpam-5895	123	23	the	the	DET
ejpam-5895	123	24	gfem	gfem	NOUN
ejpam-5895	123	25	works	work	VERB
ejpam-5895	123	26	better	well	ADV
ejpam-5895	123	27	than	than	ADP
ejpam-5895	123	28	fdm	fdm	NOUN
ejpam-5895	123	29	and	and	CCONJ
ejpam-5895	123	30	approximation	approximation	NOUN
ejpam-5895	123	31	s.	s.	PROPN
ejpam-5895	123	32	s.	s.	PROPN
ejpam-5895	123	33	almutairi	almutairi	PROPN
ejpam-5895	123	34	,	,	PUNCT
ejpam-5895	123	35	a.	a.	PROPN
ejpam-5895	123	36	m.	m.	PROPN
ejpam-5895	123	37	saeed	saeed	PROPN
ejpam-5895	123	38	/	/	SYM
ejpam-5895	123	39	eur	eur	PROPN
ejpam-5895	123	40	.	.	PUNCT
ejpam-5895	124	1	j.	j.	PROPN
ejpam-5895	124	2	pure	pure	PROPN
ejpam-5895	124	3	appl	appl	PROPN
ejpam-5895	124	4	.	.	PROPN
ejpam-5895	124	5	math	math	PROPN
ejpam-5895	124	6	,	,	PUNCT
ejpam-5895	124	7	18	18	NUM
ejpam-5895	124	8	(	(	PUNCT
ejpam-5895	124	9	2	2	NUM
ejpam-5895	124	10	)	)	PUNCT
ejpam-5895	124	11	(	(	PUNCT
ejpam-5895	124	12	2025	2025	NUM
ejpam-5895	124	13	)	)	PUNCT
ejpam-5895	124	14	,	,	PUNCT
ejpam-5895	124	15	5895	5895	NUM
ejpam-5895	124	16	8	8	NUM
ejpam-5895	124	17	of	of	ADP
ejpam-5895	124	18	10	10	NUM
ejpam-5895	124	19	solution	solution	NOUN
ejpam-5895	124	20	from	from	ADP
ejpam-5895	124	21	gfem	gfem	PROPN
ejpam-5895	124	22	is	be	AUX
ejpam-5895	124	23	very	very	ADV
ejpam-5895	124	24	close	close	ADJ
ejpam-5895	124	25	to	to	ADP
ejpam-5895	124	26	the	the	DET
ejpam-5895	124	27	analytical	analytical	ADJ
ejpam-5895	124	28	solution	solution	NOUN
ejpam-5895	124	29	which	which	PRON
ejpam-5895	124	30	support	support	VERB
ejpam-5895	124	31	our	our	PRON
ejpam-5895	124	32	result	result	NOUN
ejpam-5895	124	33	.	.	PUNCT
ejpam-5895	125	1	figure	figure	VERB
ejpam-5895	125	2	4	4	NUM
ejpam-5895	125	3	:	:	PUNCT
ejpam-5895	125	4	graph	graph	NOUN
ejpam-5895	125	5	of	of	ADP
ejpam-5895	125	6	the	the	DET
ejpam-5895	125	7	numerical	numerical	ADJ
ejpam-5895	125	8	solution	solution	NOUN
ejpam-5895	125	9	of	of	ADP
ejpam-5895	125	10	poisson	poisson	NOUN
ejpam-5895	125	11	equation	equation	NOUN
ejpam-5895	125	12	using	use	VERB
ejpam-5895	125	13	fdm	fdm	NOUN
ejpam-5895	125	14	.	.	PUNCT
ejpam-5895	126	1	figure	figure	VERB
ejpam-5895	126	2	5	5	NUM
ejpam-5895	126	3	:	:	PUNCT
ejpam-5895	126	4	graph	graph	NOUN
ejpam-5895	126	5	of	of	ADP
ejpam-5895	126	6	the	the	DET
ejpam-5895	126	7	numerical	numerical	ADJ
ejpam-5895	126	8	solution	solution	NOUN
ejpam-5895	126	9	of	of	ADP
ejpam-5895	126	10	poisson	poisson	NOUN
ejpam-5895	126	11	equation	equation	NOUN
ejpam-5895	126	12	using	use	VERB
ejpam-5895	126	13	gfem	gfem	PROPN
ejpam-5895	126	14	.	.	PUNCT
ejpam-5895	127	1	s.	s.	PROPN
ejpam-5895	127	2	s.	s.	PROPN
ejpam-5895	127	3	almutairi	almutairi	PROPN
ejpam-5895	127	4	,	,	PUNCT
ejpam-5895	127	5	a.	a.	PROPN
ejpam-5895	127	6	m.	m.	PROPN
ejpam-5895	127	7	saeed	saeed	PROPN
ejpam-5895	127	8	/	/	SYM
ejpam-5895	127	9	eur	eur	PROPN
ejpam-5895	127	10	.	.	PUNCT
ejpam-5895	128	1	j.	j.	PROPN
ejpam-5895	128	2	pure	pure	PROPN
ejpam-5895	128	3	appl	appl	PROPN
ejpam-5895	128	4	.	.	PROPN
ejpam-5895	128	5	math	math	PROPN
ejpam-5895	128	6	,	,	PUNCT
ejpam-5895	128	7	18	18	NUM
ejpam-5895	128	8	(	(	PUNCT
ejpam-5895	128	9	2	2	NUM
ejpam-5895	128	10	)	)	PUNCT
ejpam-5895	128	11	(	(	PUNCT
ejpam-5895	128	12	2025	2025	NUM
ejpam-5895	128	13	)	)	PUNCT
ejpam-5895	128	14	,	,	PUNCT
ejpam-5895	128	15	5895	5895	NUM
ejpam-5895	128	16	9	9	NUM
ejpam-5895	128	17	of	of	ADP
ejpam-5895	128	18	10	10	NUM
ejpam-5895	128	19	figure	figure	NOUN
ejpam-5895	128	20	6	6	NUM
ejpam-5895	128	21	:	:	PUNCT
ejpam-5895	128	22	graph	graph	NOUN
ejpam-5895	128	23	of	of	ADP
ejpam-5895	128	24	the	the	DET
ejpam-5895	128	25	analytical	analytical	ADJ
ejpam-5895	128	26	solution	solution	NOUN
ejpam-5895	128	27	.	.	PUNCT
ejpam-5895	129	1	5	5	X
ejpam-5895	129	2	.	.	X
ejpam-5895	129	3	conclusion	conclusion	NOUN
ejpam-5895	129	4	in	in	ADP
ejpam-5895	129	5	this	this	DET
ejpam-5895	129	6	paper	paper	NOUN
ejpam-5895	129	7	,	,	PUNCT
ejpam-5895	129	8	we	we	PRON
ejpam-5895	129	9	have	have	AUX
ejpam-5895	129	10	applied	apply	VERB
ejpam-5895	129	11	galerkin	galerkin	ADJ
ejpam-5895	129	12	finite	finite	PROPN
ejpam-5895	129	13	element	element	NOUN
ejpam-5895	129	14	method	method	NOUN
ejpam-5895	129	15	for	for	ADP
ejpam-5895	129	16	solving	solve	VERB
ejpam-5895	129	17	poisson	poisson	NOUN
ejpam-5895	129	18	equation	equation	NOUN
ejpam-5895	129	19	,	,	PUNCT
ejpam-5895	129	20	the	the	DET
ejpam-5895	129	21	numerical	numerical	ADJ
ejpam-5895	129	22	experiments	experiment	NOUN
ejpam-5895	129	23	conducted	conduct	VERB
ejpam-5895	129	24	on	on	ADP
ejpam-5895	129	25	both	both	CCONJ
ejpam-5895	129	26	gfem	gfem	NOUN
ejpam-5895	129	27	and	and	CCONJ
ejpam-5895	129	28	fdm	fdm	VERB
ejpam-5895	129	29	for	for	ADP
ejpam-5895	129	30	comparison	comparison	NOUN
ejpam-5895	129	31	purpose	purpose	NOUN
ejpam-5895	129	32	.	.	PUNCT
ejpam-5895	130	1	the	the	DET
ejpam-5895	130	2	results	result	NOUN
ejpam-5895	130	3	reveal	reveal	VERB
ejpam-5895	130	4	that	that	SCONJ
ejpam-5895	130	5	the	the	DET
ejpam-5895	130	6	gfem	gfem	NOUN
ejpam-5895	130	7	is	be	AUX
ejpam-5895	130	8	more	more	ADV
ejpam-5895	130	9	superior	superior	ADJ
ejpam-5895	130	10	than	than	ADP
ejpam-5895	130	11	fdm	fdm	NOUN
ejpam-5895	130	12	depends	depend	VERB
ejpam-5895	130	13	on	on	ADP
ejpam-5895	130	14	its	its	PRON
ejpam-5895	130	15	accuracy	accuracy	NOUN
ejpam-5895	130	16	.	.	PUNCT
ejpam-5895	131	1	we	we	PRON
ejpam-5895	131	2	conclude	conclude	VERB
ejpam-5895	131	3	that	that	SCONJ
ejpam-5895	131	4	gfem	gfem	PROPN
ejpam-5895	131	5	is	be	AUX
ejpam-5895	131	6	a	a	DET
ejpam-5895	131	7	good	good	ADJ
ejpam-5895	131	8	alternative	alternative	ADJ
ejpam-5895	131	9	method	method	NOUN
ejpam-5895	131	10	for	for	ADP
ejpam-5895	131	11	solving	solve	VERB
ejpam-5895	131	12	pdes	pde	NOUN
ejpam-5895	131	13	of	of	ADP
ejpam-5895	131	14	elliptic	elliptic	ADJ
ejpam-5895	131	15	types	type	NOUN
ejpam-5895	131	16	and	and	CCONJ
ejpam-5895	131	17	we	we	PRON
ejpam-5895	131	18	can	can	AUX
ejpam-5895	131	19	extend	extend	VERB
ejpam-5895	131	20	this	this	DET
ejpam-5895	131	21	work	work	NOUN
ejpam-5895	131	22	for	for	ADP
ejpam-5895	131	23	solving	solve	VERB
ejpam-5895	131	24	several	several	ADJ
ejpam-5895	131	25	types	type	NOUN
ejpam-5895	131	26	of	of	ADP
ejpam-5895	131	27	equations	equation	NOUN
ejpam-5895	131	28	which	which	PRON
ejpam-5895	131	29	applied	apply	VERB
ejpam-5895	131	30	for	for	ADP
ejpam-5895	131	31	many	many	ADJ
ejpam-5895	131	32	fields	field	NOUN
ejpam-5895	131	33	of	of	ADP
ejpam-5895	131	34	engineering	engineering	NOUN
ejpam-5895	131	35	,	,	PUNCT
ejpam-5895	131	36	fluid	fluid	ADJ
ejpam-5895	131	37	dynamics	dynamic	NOUN
ejpam-5895	131	38	.	.	PUNCT
ejpam-5895	131	39	.	.	PUNCT
ejpam-5895	131	40	.	.	PUNCT
ejpam-5895	132	1	etc	etc	X
ejpam-5895	132	2	.	.	X
ejpam-5895	133	1	acknowledgements	acknowledgement	VERB
ejpam-5895	133	2	the	the	DET
ejpam-5895	133	3	researchers	researcher	NOUN
ejpam-5895	133	4	would	would	AUX
ejpam-5895	133	5	like	like	VERB
ejpam-5895	133	6	to	to	PART
ejpam-5895	133	7	thank	thank	VERB
ejpam-5895	133	8	the	the	DET
ejpam-5895	133	9	deanship	deanship	NOUN
ejpam-5895	133	10	of	of	ADP
ejpam-5895	133	11	graduate	graduate	NOUN
ejpam-5895	133	12	studies	study	NOUN
ejpam-5895	133	13	and	and	CCONJ
ejpam-5895	133	14	scientific	scientific	ADJ
ejpam-5895	133	15	research	research	NOUN
ejpam-5895	133	16	at	at	ADP
ejpam-5895	133	17	qassim	qassim	PROPN
ejpam-5895	133	18	university	university	PROPN
ejpam-5895	133	19	for	for	ADP
ejpam-5895	133	20	financial	financial	ADJ
ejpam-5895	133	21	support	support	NOUN
ejpam-5895	133	22	(	(	PUNCT
ejpam-5895	133	23	qu	qu	NOUN
ejpam-5895	133	24	-	-	NOUN
ejpam-5895	133	25	apc-2025	apc-2025	NOUN
ejpam-5895	133	26	)	)	PUNCT
ejpam-5895	133	27	.	.	PUNCT
ejpam-5895	134	1	references	reference	NOUN
ejpam-5895	134	2	[	[	X
ejpam-5895	134	3	1	1	X
ejpam-5895	134	4	]	]	PUNCT
ejpam-5895	134	5	a	a	DET
ejpam-5895	134	6	quarteroni	quarteroni	NOUN
ejpam-5895	134	7	.	.	PUNCT
ejpam-5895	135	1	numerical	numerical	ADJ
ejpam-5895	135	2	approximation	approximation	NOUN
ejpam-5895	135	3	of	of	ADP
ejpam-5895	135	4	partial	partial	ADJ
ejpam-5895	135	5	differential	differential	ADJ
ejpam-5895	135	6	equations	equation	NOUN
ejpam-5895	135	7	.	.	PUNCT
ejpam-5895	136	1	berlin	berlin	PROPN
ejpam-5895	136	2	;	;	PUNCT
ejpam-5895	136	3	new	new	PROPN
ejpam-5895	136	4	york	york	PROPN
ejpam-5895	136	5	:	:	PUNCT
ejpam-5895	136	6	springer	springer	NOUN
ejpam-5895	136	7	-	-	PUNCT
ejpam-5895	136	8	verlag	verlag	PROPN
ejpam-5895	136	9	,	,	PUNCT
ejpam-5895	136	10	1994	1994	NUM
ejpam-5895	136	11	.	.	PUNCT
ejpam-5895	137	1	[	[	X
ejpam-5895	137	2	2	2	NUM
ejpam-5895	137	3	]	]	PUNCT
ejpam-5895	137	4	g	g	PROPN
ejpam-5895	137	5	smith	smith	PROPN
ejpam-5895	137	6	.	.	PUNCT
ejpam-5895	138	1	numerical	numerical	ADJ
ejpam-5895	138	2	solution	solution	NOUN
ejpam-5895	138	3	of	of	ADP
ejpam-5895	138	4	partial	partial	ADJ
ejpam-5895	138	5	differential	differential	NOUN
ejpam-5895	138	6	equations	equation	NOUN
ejpam-5895	138	7	:	:	PUNCT
ejpam-5895	138	8	finite	finite	ADJ
ejpam-5895	138	9	difference	difference	NOUN
ejpam-5895	138	10	methods	method	NOUN
ejpam-5895	138	11	.	.	PUNCT
ejpam-5895	139	1	clarendon	clarendon	PROPN
ejpam-5895	139	2	press	press	PROPN
ejpam-5895	139	3	,	,	PUNCT
ejpam-5895	139	4	1985	1985	NUM
ejpam-5895	139	5	.	.	PUNCT
ejpam-5895	140	1	[	[	X
ejpam-5895	140	2	3	3	NUM
ejpam-5895	140	3	]	]	SYM
ejpam-5895	140	4	b	b	PROPN
ejpam-5895	140	5	szabo	szabo	PROPN
ejpam-5895	140	6	and	and	CCONJ
ejpam-5895	140	7	i	i	PROPN
ejpam-5895	140	8	babuska	babuska	PROPN
ejpam-5895	140	9	.	.	PUNCT
ejpam-5895	141	1	finite	finite	PROPN
ejpam-5895	141	2	element	element	NOUN
ejpam-5895	141	3	analysis	analysis	NOUN
ejpam-5895	141	4	:	:	PUNCT
ejpam-5895	141	5	method	method	NOUN
ejpam-5895	141	6	,	,	PUNCT
ejpam-5895	141	7	verification	verification	NOUN
ejpam-5895	141	8	and	and	CCONJ
ejpam-5895	141	9	validation	validation	NOUN
ejpam-5895	141	10	.	.	PUNCT
ejpam-5895	142	1	wiley	wiley	PROPN
ejpam-5895	142	2	,	,	PUNCT
ejpam-5895	142	3	2021	2021	NUM
ejpam-5895	142	4	.	.	PUNCT
ejpam-5895	143	1	[	[	X
ejpam-5895	143	2	4	4	NUM
ejpam-5895	143	3	]	]	PUNCT
ejpam-5895	143	4	e	e	X
ejpam-5895	143	5	cheney	cheney	NOUN
ejpam-5895	143	6	and	and	CCONJ
ejpam-5895	143	7	d	d	PROPN
ejpam-5895	143	8	kincaid	kincaid	PROPN
ejpam-5895	143	9	.	.	PUNCT
ejpam-5895	144	1	numerical	numerical	PROPN
ejpam-5895	144	2	mathematics	mathematics	PROPN
ejpam-5895	144	3	and	and	CCONJ
ejpam-5895	144	4	computing	computing	NOUN
ejpam-5895	144	5	.	.	PUNCT
ejpam-5895	145	1	pacific	pacific	PROPN
ejpam-5895	145	2	grove	grove	PROPN
ejpam-5895	145	3	,	,	PUNCT
ejpam-5895	145	4	ca	can	AUX
ejpam-5895	145	5	:	:	PUNCT
ejpam-5895	145	6	brooks	brooks	PROPN
ejpam-5895	145	7	/	/	SYM
ejpam-5895	145	8	cole	cole	PROPN
ejpam-5895	145	9	pub	pub	NOUN
ejpam-5895	145	10	.	.	PUNCT
ejpam-5895	146	1	co	co	NOUN
ejpam-5895	146	2	,	,	PUNCT
ejpam-5895	146	3	1999	1999	NUM
ejpam-5895	146	4	.	.	PUNCT
ejpam-5895	147	1	s.	s.	PROPN
ejpam-5895	147	2	s.	s.	PROPN
ejpam-5895	147	3	almutairi	almutairi	PROPN
ejpam-5895	147	4	,	,	PUNCT
ejpam-5895	147	5	a.	a.	PROPN
ejpam-5895	147	6	m.	m.	PROPN
ejpam-5895	147	7	saeed	saeed	PROPN
ejpam-5895	147	8	/	/	SYM
ejpam-5895	147	9	eur	eur	PROPN
ejpam-5895	147	10	.	.	PUNCT
ejpam-5895	148	1	j.	j.	PROPN
ejpam-5895	148	2	pure	pure	PROPN
ejpam-5895	148	3	appl	appl	PROPN
ejpam-5895	148	4	.	.	PROPN
ejpam-5895	148	5	math	math	PROPN
ejpam-5895	148	6	,	,	PUNCT
ejpam-5895	148	7	18	18	NUM
ejpam-5895	148	8	(	(	PUNCT
ejpam-5895	148	9	2	2	NUM
ejpam-5895	148	10	)	)	PUNCT
ejpam-5895	148	11	(	(	PUNCT
ejpam-5895	148	12	2025	2025	NUM
ejpam-5895	148	13	)	)	PUNCT
ejpam-5895	148	14	,	,	PUNCT
ejpam-5895	148	15	5895	5895	NUM
ejpam-5895	148	16	10	10	NUM
ejpam-5895	148	17	of	of	ADP
ejpam-5895	148	18	10	10	NUM
ejpam-5895	148	19	[	[	SYM
ejpam-5895	148	20	5	5	NUM
ejpam-5895	148	21	]	]	X
ejpam-5895	148	22	k	k	NOUN
ejpam-5895	148	23	bathe	bathe	VERB
ejpam-5895	148	24	.	.	PUNCT
ejpam-5895	149	1	finite	finite	PROPN
ejpam-5895	149	2	element	element	NOUN
ejpam-5895	149	3	procedures	procedure	NOUN
ejpam-5895	149	4	.	.	PUNCT
ejpam-5895	150	1	klaus	klaus	PROPN
ejpam-5895	150	2	-	-	PUNCT
ejpam-5895	150	3	jurgen	jurgen	PROPN
ejpam-5895	150	4	bathe	bathe	VERB
ejpam-5895	150	5	,	,	PUNCT
ejpam-5895	150	6	2006	2006	NUM
ejpam-5895	150	7	.	.	PUNCT
ejpam-5895	151	1	[	[	X
ejpam-5895	151	2	6	6	NUM
ejpam-5895	151	3	]	]	PUNCT
ejpam-5895	151	4	p	p	NOUN
ejpam-5895	151	5	causon	causon	NOUN
ejpam-5895	151	6	and	and	CCONJ
ejpam-5895	151	7	p	p	PROPN
ejpam-5895	151	8	mingham	mingham	NOUN
ejpam-5895	151	9	.	.	PUNCT
ejpam-5895	152	1	introductory	introductory	ADJ
ejpam-5895	152	2	finite	finite	ADJ
ejpam-5895	152	3	difference	difference	NOUN
ejpam-5895	152	4	methods	method	NOUN
ejpam-5895	152	5	for	for	ADP
ejpam-5895	152	6	pdes	pde	NOUN
ejpam-5895	152	7	.	.	PUNCT
ejpam-5895	153	1	bookboon	bookboon	NOUN
ejpam-5895	153	2	,	,	PUNCT
ejpam-5895	153	3	2010	2010	NUM
ejpam-5895	153	4	.	.	PUNCT
ejpam-5895	154	1	[	[	X
ejpam-5895	154	2	7	7	X
ejpam-5895	154	3	]	]	SYM
ejpam-5895	154	4	u	u	NOUN
ejpam-5895	154	5	yashkun	yashkun	NOUN
ejpam-5895	154	6	and	and	CCONJ
ejpam-5895	154	7	m	m	PROPN
ejpam-5895	154	8	chandio	chandio	NOUN
ejpam-5895	154	9	.	.	PUNCT
ejpam-5895	155	1	finite	finite	ADJ
ejpam-5895	155	2	difference	difference	NOUN
ejpam-5895	155	3	method	method	NOUN
ejpam-5895	155	4	with	with	ADP
ejpam-5895	155	5	dirichlet	dirichlet	PROPN
ejpam-5895	155	6	problems	problem	NOUN
ejpam-5895	155	7	of	of	ADP
ejpam-5895	155	8	2d	2d	NUM
ejpam-5895	155	9	laplace	laplace	NOUN
ejpam-5895	155	10	’s	’s	PART
ejpam-5895	155	11	equation	equation	NOUN
ejpam-5895	155	12	in	in	ADP
ejpam-5895	155	13	elliptic	elliptic	ADJ
ejpam-5895	155	14	domain	domain	NOUN
ejpam-5895	155	15	.	.	PUNCT
ejpam-5895	156	1	pakistan	pakistan	PROPN
ejpam-5895	156	2	journal	journal	PROPN
ejpam-5895	156	3	of	of	ADP
ejpam-5895	156	4	engineering	engineering	NOUN
ejpam-5895	156	5	technology	technology	NOUN
ejpam-5895	156	6	and	and	CCONJ
ejpam-5895	156	7	science	science	NOUN
ejpam-5895	156	8	(	(	PUNCT
ejpam-5895	156	9	pjets	pjet	NOUN
ejpam-5895	156	10	)	)	PUNCT
ejpam-5895	156	11	,	,	PUNCT
ejpam-5895	156	12	6(2):136–144	6(2):136–144	NOUN
ejpam-5895	156	13	,	,	PUNCT
ejpam-5895	156	14	2016	2016	NUM
ejpam-5895	156	15	.	.	PUNCT
ejpam-5895	157	1	[	[	X
ejpam-5895	157	2	8	8	NUM
ejpam-5895	157	3	]	]	PUNCT
ejpam-5895	157	4	t	t	PROPN
ejpam-5895	157	5	hughes	hughe	NOUN
ejpam-5895	157	6	.	.	PUNCT
ejpam-5895	158	1	the	the	DET
ejpam-5895	158	2	finite	finite	PROPN
ejpam-5895	158	3	element	element	NOUN
ejpam-5895	158	4	method	method	NOUN
ejpam-5895	158	5	:	:	PUNCT
ejpam-5895	158	6	linear	linear	ADJ
ejpam-5895	158	7	static	static	ADJ
ejpam-5895	158	8	and	and	CCONJ
ejpam-5895	158	9	dynamic	dynamic	ADJ
ejpam-5895	158	10	finite	finite	NOUN
ejpam-5895	158	11	element	element	NOUN
ejpam-5895	158	12	analysis	analysis	NOUN
ejpam-5895	158	13	.	.	PUNCT
ejpam-5895	159	1	mineola	mineola	PROPN
ejpam-5895	159	2	,	,	PUNCT
ejpam-5895	159	3	ny	ny	PROPN
ejpam-5895	159	4	:	:	PUNCT
ejpam-5895	159	5	dover	dover	PROPN
ejpam-5895	159	6	publications	publication	NOUN
ejpam-5895	159	7	,	,	PUNCT
ejpam-5895	159	8	2000	2000	NUM
ejpam-5895	159	9	.	.	PUNCT
ejpam-5895	160	1	[	[	X
ejpam-5895	160	2	9	9	NUM
ejpam-5895	160	3	]	]	X
ejpam-5895	160	4	o	o	NOUN
ejpam-5895	160	5	zienkiewicz	zienkiewicz	NOUN
ejpam-5895	160	6	,	,	PUNCT
ejpam-5895	160	7	r	r	PROPN
ejpam-5895	160	8	taylor	taylor	PROPN
ejpam-5895	160	9	,	,	PUNCT
ejpam-5895	160	10	and	and	CCONJ
ejpam-5895	160	11	j	j	PROPN
ejpam-5895	160	12	zhu	zhu	PROPN
ejpam-5895	160	13	.	.	PUNCT
ejpam-5895	161	1	the	the	DET
ejpam-5895	161	2	finite	finite	PROPN
ejpam-5895	161	3	element	element	NOUN
ejpam-5895	161	4	method	method	NOUN
ejpam-5895	161	5	:	:	PUNCT
ejpam-5895	161	6	its	its	PRON
ejpam-5895	161	7	basis	basis	NOUN
ejpam-5895	161	8	and	and	CCONJ
ejpam-5895	161	9	fundamentals	fundamental	NOUN
ejpam-5895	161	10	.	.	PUNCT
ejpam-5895	162	1	elsevier	elsevier	PROPN
ejpam-5895	162	2	science	science	PROPN
ejpam-5895	162	3	,	,	PUNCT
ejpam-5895	162	4	2005	2005	NUM
ejpam-5895	162	5	.	.	PUNCT
ejpam-5895	163	1	[	[	X
ejpam-5895	163	2	10	10	NUM
ejpam-5895	163	3	]	]	X
ejpam-5895	163	4	s	s	PART
ejpam-5895	163	5	brenner	brenner	NOUN
ejpam-5895	163	6	and	and	CCONJ
ejpam-5895	163	7	r	r	PROPN
ejpam-5895	163	8	scott	scott	PROPN
ejpam-5895	163	9	.	.	PUNCT
ejpam-5895	164	1	the	the	DET
ejpam-5895	164	2	mathematical	mathematical	ADJ
ejpam-5895	164	3	theory	theory	NOUN
ejpam-5895	164	4	of	of	ADP
ejpam-5895	164	5	finite	finite	ADJ
ejpam-5895	164	6	element	element	NOUN
ejpam-5895	164	7	methods	method	NOUN
ejpam-5895	164	8	.	.	PUNCT
ejpam-5895	165	1	springer	springer	PROPN
ejpam-5895	165	2	new	new	PROPN
ejpam-5895	165	3	york	york	PROPN
ejpam-5895	165	4	,	,	PUNCT
ejpam-5895	165	5	2007	2007	NUM
ejpam-5895	165	6	.	.	PUNCT
ejpam-5895	166	1	[	[	X
ejpam-5895	166	2	11	11	NUM
ejpam-5895	166	3	]	]	X
ejpam-5895	166	4	r	r	NOUN
ejpam-5895	166	5	haberman	haberman	NOUN
ejpam-5895	166	6	.	.	PUNCT
ejpam-5895	167	1	elementary	elementary	PROPN
ejpam-5895	167	2	applied	apply	VERB
ejpam-5895	167	3	partial	partial	ADJ
ejpam-5895	167	4	differential	differential	NOUN
ejpam-5895	167	5	equations	equation	NOUN
ejpam-5895	167	6	:	:	PUNCT
ejpam-5895	167	7	with	with	ADP
ejpam-5895	167	8	fourier	fourier	ADJ
ejpam-5895	167	9	series	series	NOUN
ejpam-5895	167	10	and	and	CCONJ
ejpam-5895	167	11	boundary	boundary	ADJ
ejpam-5895	167	12	value	value	NOUN
ejpam-5895	167	13	problems	problem	NOUN
ejpam-5895	167	14	.	.	PUNCT
ejpam-5895	168	1	prentice	prentice	PROPN
ejpam-5895	168	2	hall	hall	PROPN
ejpam-5895	168	3	,	,	PUNCT
ejpam-5895	168	4	1998	1998	NUM
ejpam-5895	168	5	.	.	PUNCT
ejpam-5895	169	1	[	[	X
ejpam-5895	169	2	12	12	NUM
ejpam-5895	169	3	]	]	X
ejpam-5895	169	4	o	o	NOUN
ejpam-5895	169	5	zienkiewicz	zienkiewicz	NOUN
ejpam-5895	169	6	.	.	PUNCT
ejpam-5895	170	1	the	the	DET
ejpam-5895	170	2	finite	finite	PROPN
ejpam-5895	170	3	element	element	NOUN
ejpam-5895	170	4	method	method	NOUN
ejpam-5895	170	5	.	.	PUNCT
ejpam-5895	171	1	singapore	singapore	PROPN
ejpam-5895	171	2	:	:	PUNCT
ejpam-5895	171	3	mcgraw	mcgraw	PROPN
ejpam-5895	171	4	-	-	PUNCT
ejpam-5895	171	5	hill	hill	NOUN
ejpam-5895	171	6	,	,	PUNCT
ejpam-5895	171	7	1989	1989	NUM
ejpam-5895	171	8	.	.	PUNCT
ejpam-5895	172	1	[	[	X
ejpam-5895	172	2	13	13	NUM
ejpam-5895	172	3	]	]	X
ejpam-5895	172	4	k	k	NOUN
ejpam-5895	172	5	bathe	bathe	VERB
ejpam-5895	172	6	.	.	PUNCT
ejpam-5895	173	1	computational	computational	ADJ
ejpam-5895	173	2	fluid	fluid	NOUN
ejpam-5895	173	3	and	and	CCONJ
ejpam-5895	173	4	solid	solid	ADJ
ejpam-5895	173	5	mechanics	mechanic	NOUN
ejpam-5895	173	6	2003	2003	NUM
ejpam-5895	173	7	.	.	PUNCT
ejpam-5895	174	1	elsevier	elsevier	PROPN
ejpam-5895	174	2	science	science	PROPN
ejpam-5895	174	3	,	,	PUNCT
ejpam-5895	174	4	2003	2003	NUM
ejpam-5895	174	5	.	.	PUNCT
ejpam-5895	175	1	[	[	X
ejpam-5895	175	2	14	14	NUM
ejpam-5895	175	3	]	]	X
ejpam-5895	175	4	h	h	NOUN
ejpam-5895	175	5	grosshans	grosshan	NOUN
ejpam-5895	175	6	,	,	PUNCT
ejpam-5895	175	7	s	s	VERB
ejpam-5895	175	8	gopireddy	gopireddy	NOUN
ejpam-5895	175	9	,	,	PUNCT
ejpam-5895	175	10	r	r	NOUN
ejpam-5895	175	11	humza	humza	NOUN
ejpam-5895	175	12	,	,	PUNCT
ejpam-5895	175	13	and	and	CCONJ
ejpam-5895	175	14	e	e	NOUN
ejpam-5895	175	15	gutheil	gutheil	NOUN
ejpam-5895	175	16	.	.	PUNCT
ejpam-5895	176	1	modeling	modeling	NOUN
ejpam-5895	176	2	and	and	CCONJ
ejpam-5895	176	3	simulation	simulation	NOUN
ejpam-5895	176	4	of	of	ADP
ejpam-5895	176	5	single	single	ADJ
ejpam-5895	176	6	particle	particle	NOUN
ejpam-5895	176	7	and	and	CCONJ
ejpam-5895	176	8	spray	spray	VERB
ejpam-5895	176	9	drying	dry	VERB
ejpam-5895	176	10	of	of	ADP
ejpam-5895	176	11	pvpand	pvpand	NOUN
ejpam-5895	176	12	mannitol	mannitol	NOUN
ejpam-5895	176	13	-	-	PUNCT
ejpam-5895	176	14	water	water	NOUN
ejpam-5895	176	15	in	in	ADP
ejpam-5895	176	16	hot	hot	ADJ
ejpam-5895	176	17	air	air	NOUN
ejpam-5895	176	18	.	.	PUNCT
ejpam-5895	177	1	springer	springer	NOUN
ejpam-5895	177	2	,	,	PUNCT
ejpam-5895	177	3	2016	2016	NUM
ejpam-5895	177	4	.	.	PUNCT
ejpam-5895	178	1	[	[	X
ejpam-5895	178	2	15	15	NUM
ejpam-5895	178	3	]	]	X
ejpam-5895	178	4	a	a	DET
ejpam-5895	178	5	azadi	azadi	NOUN
ejpam-5895	178	6	,	,	PUNCT
ejpam-5895	178	7	a	a	DET
ejpam-5895	178	8	irani	irani	NOUN
ejpam-5895	178	9	,	,	PUNCT
ejpam-5895	178	10	m	m	NOUN
ejpam-5895	178	11	azarafza	azarafza	NOUN
ejpam-5895	178	12	,	,	PUNCT
ejpam-5895	178	13	and	and	CCONJ
ejpam-5895	178	14	m	m	PRON
ejpam-5895	178	15	bonab	bonab	NOUN
ejpam-5895	178	16	.	.	PUNCT
ejpam-5895	179	1	coupled	couple	VERB
ejpam-5895	179	2	numerical	numerical	ADJ
ejpam-5895	179	3	and	and	CCONJ
ejpam-5895	179	4	analytical	analytical	ADJ
ejpam-5895	179	5	stability	stability	NOUN
ejpam-5895	179	6	analysis	analysis	NOUN
ejpam-5895	179	7	charts	chart	NOUN
ejpam-5895	179	8	for	for	ADP
ejpam-5895	179	9	an	an	DET
ejpam-5895	179	10	earth	earth	NOUN
ejpam-5895	179	11	-	-	PUNCT
ejpam-5895	179	12	fill	fill	NOUN
ejpam-5895	179	13	dam	dam	NOUN
ejpam-5895	179	14	under	under	ADP
ejpam-5895	179	15	rapid	rapid	ADJ
ejpam-5895	179	16	drawdown	drawdown	ADJ
ejpam-5895	179	17	conditions	condition	NOUN
ejpam-5895	179	18	.	.	PUNCT
ejpam-5895	180	1	applied	apply	VERB
ejpam-5895	180	2	sciences	science	NOUN
ejpam-5895	180	3	,	,	PUNCT
ejpam-5895	180	4	12(9):19	12(9):19	NUM
ejpam-5895	180	5	,	,	PUNCT
ejpam-5895	180	6	2022	2022	NUM
ejpam-5895	180	7	.	.	PUNCT
ejpam-5895	181	1	[	[	X
ejpam-5895	181	2	16	16	NUM
ejpam-5895	181	3	]	]	X
ejpam-5895	181	4	s	s	VERB
ejpam-5895	181	5	abdulkafi	abdulkafi	NOUN
ejpam-5895	181	6	.	.	PUNCT
ejpam-5895	182	1	improved	improve	VERB
ejpam-5895	182	2	rotated	rotate	VERB
ejpam-5895	182	3	finite	finite	ADJ
ejpam-5895	182	4	difference	difference	NOUN
ejpam-5895	182	5	method	method	NOUN
ejpam-5895	182	6	for	for	ADP
ejpam-5895	182	7	solving	solve	VERB
ejpam-5895	182	8	fractional	fractional	ADJ
ejpam-5895	182	9	elliptic	elliptic	ADJ
ejpam-5895	182	10	partial	partial	ADJ
ejpam-5895	182	11	differential	differential	NOUN
ejpam-5895	182	12	equations	equation	NOUN
ejpam-5895	182	13	.	.	PUNCT
ejpam-5895	183	1	american	american	ADJ
ejpam-5895	183	2	scientific	scientific	ADJ
ejpam-5895	183	3	research	research	PROPN
ejpam-5895	183	4	journal	journal	NOUN
ejpam-5895	183	5	for	for	ADP
ejpam-5895	183	6	engineering	engineering	NOUN
ejpam-5895	183	7	,	,	PUNCT
ejpam-5895	183	8	technology	technology	NOUN
ejpam-5895	183	9	,	,	PUNCT
ejpam-5895	183	10	and	and	CCONJ
ejpam-5895	183	11	sciences	science	NOUN
ejpam-5895	183	12	(	(	PUNCT
ejpam-5895	183	13	asrjets	asrjet	NOUN
ejpam-5895	183	14	)	)	PUNCT
ejpam-5895	183	15	,	,	PUNCT
ejpam-5895	183	16	26(1):261–270	26(1):261–270	NUM
ejpam-5895	183	17	,	,	PUNCT
ejpam-5895	183	18	2016	2016	NUM
ejpam-5895	183	19	.	.	PUNCT
ejpam-5895	184	1	[	[	X
ejpam-5895	184	2	17	17	NUM
ejpam-5895	184	3	]	]	X
ejpam-5895	184	4	s	s	PART
ejpam-5895	184	5	abdulkafi	abdulkafi	NOUN
ejpam-5895	184	6	.	.	PUNCT
ejpam-5895	185	1	solving	solve	VERB
ejpam-5895	185	2	poisson	poisson	NOUN
ejpam-5895	185	3	’s	’s	PART
ejpam-5895	185	4	equation	equation	NOUN
ejpam-5895	185	5	using	use	VERB
ejpam-5895	185	6	preconditioned	precondition	VERB
ejpam-5895	185	7	nine	nine	NUM
ejpam-5895	185	8	-	-	PUNCT
ejpam-5895	185	9	point	point	NOUN
ejpam-5895	185	10	group	group	NOUN
ejpam-5895	185	11	sor	sor	NOUN
ejpam-5895	185	12	iterative	iterative	NOUN
ejpam-5895	185	13	method	method	NOUN
ejpam-5895	185	14	.	.	PUNCT
ejpam-5895	186	1	international	international	ADJ
ejpam-5895	186	2	journal	journal	PROPN
ejpam-5895	186	3	of	of	ADP
ejpam-5895	186	4	mathematics	mathematics	PROPN
ejpam-5895	186	5	and	and	CCONJ
ejpam-5895	186	6	statistics	statistic	NOUN
ejpam-5895	186	7	invention	invention	NOUN
ejpam-5895	186	8	(	(	PUNCT
ejpam-5895	186	9	ijmsi	ijmsi	NOUN
ejpam-5895	186	10	)	)	PUNCT
ejpam-5895	186	11	,	,	PUNCT
ejpam-5895	186	12	4:8	4:8	NUM
ejpam-5895	186	13	,	,	PUNCT
ejpam-5895	186	14	2016	2016	NUM
ejpam-5895	186	15	.	.	PUNCT
ejpam-5895	187	1	[	[	X
ejpam-5895	187	2	18	18	NUM
ejpam-5895	187	3	]	]	X
ejpam-5895	187	4	p	p	X
ejpam-5895	187	5	zhou	zhou	PROPN
ejpam-5895	187	6	.	.	PUNCT
ejpam-5895	188	1	finite	finite	ADJ
ejpam-5895	188	2	difference	difference	NOUN
ejpam-5895	188	3	method	method	NOUN
ejpam-5895	188	4	,	,	PUNCT
ejpam-5895	188	5	pages	page	NOUN
ejpam-5895	188	6	63–94	63–94	NUM
ejpam-5895	188	7	.	.	PUNCT
ejpam-5895	189	1	springer	springer	PROPN
ejpam-5895	189	2	berlin	berlin	PROPN
ejpam-5895	189	3	heidelberg	heidelberg	PROPN
ejpam-5895	189	4	,	,	PUNCT
ejpam-5895	189	5	berlin	berlin	PROPN
ejpam-5895	189	6	,	,	PUNCT
ejpam-5895	189	7	heidelberg	heidelberg	PROPN
ejpam-5895	189	8	,	,	PUNCT
ejpam-5895	189	9	1993	1993	NUM
ejpam-5895	189	10	.	.	PUNCT
ejpam-5895	190	1	[	[	X
ejpam-5895	190	2	19	19	NUM
ejpam-5895	190	3	]	]	X
ejpam-5895	190	4	kh	kh	PROPN
ejpam-5895	190	5	lotfy	lotfy	PROPN
ejpam-5895	190	6	,	,	PUNCT
ejpam-5895	190	7	aa	aa	PROPN
ejpam-5895	190	8	el	el	PROPN
ejpam-5895	190	9	-	-	PUNCT
ejpam-5895	190	10	bary	bary	NOUN
ejpam-5895	190	11	,	,	PUNCT
ejpam-5895	190	12	and	and	CCONJ
ejpam-5895	190	13	rs	rs	PROPN
ejpam-5895	190	14	tantawi	tantawi	PROPN
ejpam-5895	190	15	.	.	PUNCT
ejpam-5895	191	1	effects	effect	NOUN
ejpam-5895	191	2	of	of	ADP
ejpam-5895	191	3	variable	variable	ADJ
ejpam-5895	191	4	thermal	thermal	ADJ
ejpam-5895	191	5	conductivity	conductivity	NOUN
ejpam-5895	191	6	of	of	ADP
ejpam-5895	191	7	a	a	DET
ejpam-5895	191	8	small	small	ADJ
ejpam-5895	191	9	semiconductor	semiconductor	NOUN
ejpam-5895	191	10	cavity	cavity	NOUN
ejpam-5895	191	11	through	through	ADP
ejpam-5895	191	12	the	the	DET
ejpam-5895	191	13	fractional	fractional	ADJ
ejpam-5895	191	14	order	order	NOUN
ejpam-5895	191	15	heat	heat	NOUN
ejpam-5895	191	16	-	-	PUNCT
ejpam-5895	191	17	magneto	magneto	VERB
ejpam-5895	191	18	-	-	PUNCT
ejpam-5895	191	19	photothermal	photothermal	ADJ
ejpam-5895	191	20	theory	theory	NOUN
ejpam-5895	191	21	.	.	PUNCT
ejpam-5895	192	1	the	the	DET
ejpam-5895	192	2	european	european	PROPN
ejpam-5895	192	3	physical	physical	PROPN
ejpam-5895	192	4	journal	journal	PROPN
ejpam-5895	192	5	plus	plus	CCONJ
ejpam-5895	192	6	,	,	PUNCT
ejpam-5895	192	7	134(6):280	134(6):280	NUM
ejpam-5895	192	8	,	,	PUNCT
ejpam-5895	192	9	2019	2019	NUM
ejpam-5895	192	10	.	.	PUNCT
ejpam-5895	193	1	[	[	X
ejpam-5895	193	2	20	20	NUM
ejpam-5895	193	3	]	]	X
ejpam-5895	193	4	kh	kh	PROPN
ejpam-5895	193	5	lotfy	lotfy	PROPN
ejpam-5895	193	6	,	,	PUNCT
ejpam-5895	193	7	aa	aa	PROPN
ejpam-5895	193	8	el	el	PROPN
ejpam-5895	193	9	-	-	PUNCT
ejpam-5895	193	10	bary	bary	PROPN
ejpam-5895	193	11	,	,	PUNCT
ejpam-5895	193	12	w	w	PROPN
ejpam-5895	193	13	hassan	hassan	PROPN
ejpam-5895	193	14	,	,	PUNCT
ejpam-5895	193	15	and	and	CCONJ
ejpam-5895	193	16	mh	mh	PROPN
ejpam-5895	193	17	ahmed	ahmed	PROPN
ejpam-5895	193	18	.	.	PUNCT
ejpam-5895	194	1	hall	hall	PROPN
ejpam-5895	194	2	current	current	ADJ
ejpam-5895	194	3	influence	influence	NOUN
ejpam-5895	194	4	of	of	ADP
ejpam-5895	194	5	microtemperature	microtemperature	PROPN
ejpam-5895	194	6	magneto	magneto	VERB
ejpam-5895	194	7	-	-	PUNCT
ejpam-5895	194	8	elastic	elastic	ADJ
ejpam-5895	194	9	semiconductor	semiconductor	NOUN
ejpam-5895	194	10	material	material	NOUN
ejpam-5895	194	11	.	.	PUNCT
ejpam-5895	195	1	superlattices	superlattice	NOUN
ejpam-5895	195	2	and	and	CCONJ
ejpam-5895	195	3	microstructures	microstructure	NOUN
ejpam-5895	195	4	,	,	PUNCT
ejpam-5895	195	5	139:106428	139:106428	NUM
ejpam-5895	195	6	,	,	PUNCT
ejpam-5895	195	7	2020	2020	NUM
ejpam-5895	195	8	.	.	PUNCT
ejpam-5895	196	1	[	[	X
ejpam-5895	196	2	21	21	NUM
ejpam-5895	196	3	]	]	X
ejpam-5895	196	4	kh	kh	PROPN
ejpam-5895	196	5	lotfy	lotfy	PROPN
ejpam-5895	196	6	and	and	CCONJ
ejpam-5895	196	7	rs	rs	PROPN
ejpam-5895	196	8	tantawi	tantawi	PROPN
ejpam-5895	196	9	.	.	PUNCT
ejpam-5895	197	1	photo	photo	NOUN
ejpam-5895	197	2	-	-	PUNCT
ejpam-5895	197	3	thermal	thermal	ADJ
ejpam-5895	197	4	-	-	PUNCT
ejpam-5895	197	5	elastic	elastic	ADJ
ejpam-5895	197	6	interaction	interaction	NOUN
ejpam-5895	197	7	in	in	ADP
ejpam-5895	197	8	a	a	DET
ejpam-5895	197	9	functionally	functionally	ADV
ejpam-5895	197	10	graded	grade	VERB
ejpam-5895	197	11	material	material	NOUN
ejpam-5895	197	12	(	(	PUNCT
ejpam-5895	197	13	fgm	fgm	PROPN
ejpam-5895	197	14	)	)	PUNCT
ejpam-5895	197	15	and	and	CCONJ
ejpam-5895	197	16	magnetic	magnetic	ADJ
ejpam-5895	197	17	field	field	NOUN
ejpam-5895	197	18	.	.	PUNCT
ejpam-5895	198	1	silicon	silicon	NOUN
ejpam-5895	198	2	,	,	PUNCT
ejpam-5895	198	3	12(2):295–303	12(2):295–303	NUM
ejpam-5895	198	4	,	,	PUNCT
ejpam-5895	198	5	2020	2020	NUM
ejpam-5895	198	6	.	.	PUNCT
ejpam-5895	199	1	[	[	X
ejpam-5895	199	2	22	22	NUM
ejpam-5895	199	3	]	]	X
ejpam-5895	199	4	p	p	NOUN
ejpam-5895	199	5	ciarlet	ciarlet	NOUN
ejpam-5895	199	6	.	.	PUNCT
ejpam-5895	200	1	the	the	DET
ejpam-5895	200	2	finite	finite	PROPN
ejpam-5895	200	3	element	element	NOUN
ejpam-5895	200	4	method	method	NOUN
ejpam-5895	200	5	for	for	ADP
ejpam-5895	200	6	elliptic	elliptic	ADJ
ejpam-5895	200	7	problems	problem	NOUN
ejpam-5895	200	8	.	.	PUNCT
ejpam-5895	201	1	elsevier	elsevier	PROPN
ejpam-5895	201	2	science	science	PROPN
ejpam-5895	201	3	,	,	PUNCT
ejpam-5895	201	4	1978	1978	NUM
ejpam-5895	201	5	.	.	PUNCT
ejpam-5895	202	1	[	[	X
ejpam-5895	202	2	23	23	NUM
ejpam-5895	202	3	]	]	X
ejpam-5895	202	4	j	j	PROPN
ejpam-5895	202	5	guermond	guermond	NOUN
ejpam-5895	202	6	and	and	CCONJ
ejpam-5895	202	7	a	a	DET
ejpam-5895	202	8	ern	ern	PROPN
ejpam-5895	202	9	.	.	PUNCT
ejpam-5895	203	1	finite	finite	PROPN
ejpam-5895	203	2	elements	elements	PROPN
ejpam-5895	203	3	ii	ii	PROPN
ejpam-5895	203	4	:	:	PUNCT
ejpam-5895	203	5	galerkin	galerkin	ADJ
ejpam-5895	203	6	approximation	approximation	NOUN
ejpam-5895	203	7	,	,	PUNCT
ejpam-5895	203	8	elliptic	elliptic	ADJ
ejpam-5895	203	9	and	and	CCONJ
ejpam-5895	203	10	mixed	mixed	ADJ
ejpam-5895	203	11	pdes	pde	NOUN
ejpam-5895	203	12	.	.	PUNCT
ejpam-5895	204	1	springer	springer	NOUN
ejpam-5895	204	2	international	international	PROPN
ejpam-5895	204	3	,	,	PUNCT
ejpam-5895	204	4	,	,	PUNCT
ejpam-5895	204	5	2022	2022	NUM
ejpam-5895	204	6	.	.	PUNCT