Analysis of Discontinuous Galerkin Methods using Mesh-Dependent Norms and Applications to Problems with Rough Data
Numerical Analysis
2017-03-30 v2
Abstract
We prove the inf-sup stability of a discontinuous Galerkin scheme for second order elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform meshes for all spatial dimensions. This results in a priori error bounds in these norms. As an application we examine a problem with rough source term where the solution can not be characterised as a weak solution and show quasi-optimal error control.
Cite
@article{arxiv.1610.04994,
title = {Analysis of Discontinuous Galerkin Methods using Mesh-Dependent Norms and Applications to Problems with Rough Data},
author = {Emmanuil H. Georgoulis and Tristan Pryer},
journal= {arXiv preprint arXiv:1610.04994},
year = {2017}
}
Comments
10 pages, 1 figure