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|Title:||Babuška-Osborn techniques in discontinuous Galerkin methods: $L^2$-norm error estimates for unstructured meshes|
|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.|
|Rights:||Copyright © The Author(s), 2017.|
|Appears in Collections:||Published Articles, Dept. of Mathematics|
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|1704.05238v1.pdf||Pre-review (submitted draft)||1.59 MB||Adobe PDF||View/Open|
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