id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-232	Lewis, Thomas; Rapp, Aaron; Zhang, Yi	Penalty parameter and dual-wind discontinuous Galerkin approximation methods for elliptic second order PDEs	2022	16	.pdf	application/pdf	7283	331	73	By the Cauchy-Schwarz inequality and the fact that [[uch − u]]e = 0 for all e ∈ Eh, we have Bh,γ(uch − u, uch − u γ h) ≤ 1 2 ‖∇+ h,0(uch − u)‖L2(Th)‖∇+ h,0(uch − u γ h)‖L2(Th) + 1 2 ‖∇−h,0(uch − u)‖L2(Th)‖∇−h,0(uch − u γ h)‖L2(Th) + γ ∑ e∈Eh 〈h−1 e [[uch − u γ h]]‖2L2(e) ≤ Bh,γ(uch − u γ h, u c h − u γ h) = Bh,γ(uch − u, uch − u γ h) +Bh,γ(u− uγh, u c h − u γ h).	cache/ejde-232.pdf	txt/ejde-232.txt