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Title: Babuška-Osborn techniques in discontinuous Galerkin methods: $L^2$-norm error estimates for unstructured meshes
Authors: Georgoulis, Emmanuil
Makridakis, Charalambos
Pryer, Tristan
First Published: 18-Apr-2017
Citation: arXiv:1704.05238 [math.NA]
Abstract: We prove the inf-sup stability of the interior penalty class of discontinuous Galerkin schemes in unbalanced mesh-dependent norms, under a mesh condition allowing for a general class of meshes, which includes many examples of geometrically graded element neighbourhoods. The inf-sup condition results in the stability of the interior penalty Ritz projection in $L^2$ as well as, for the first time, quasi-best approximations in the $L^2$-norm which in turn imply a priori error estimates that do not depend on the global maximum meshsize in that norm. Some numerical experiments are also given.
Version: Pre-print
Type: Journal Article
Rights: Copyright © The Author(s), 2017.
Appears in Collections:Published Articles, Dept. of Mathematics

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