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Babu\v{s}ka-Osborn techniques in discontinuous Galerkin methods: $L^2$-norm error estimates for unstructured meshes. (arXiv:1704.05238v1 [math.NA])
来源于:arXiv
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. 查看全文>>
