Analysis of Discontinuous Galerkin Methods using Mesh-Dependent Norms\n and Applications to Problems with Rough Data

2016/10/17 by Emmanuil H. Georgoulis, Georgoulis, Emmanuil H., Tristan Pryer +1
Engineering · Computer Science · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods

paper · pdf · doi:10.48550/arxiv.1610.04994

Abstract

We prove the inf-sup stability of a discontinuous Galerkin scheme for second\norder elliptic operators in (unbalanced) mesh-dependent norms for quasi-uniform\nmeshes for all spatial dimensions. This results in a priori error bounds in\nthese norms. As an application we examine a problem with rough source term\nwhere the solution can not be characterised as a weak solution and show\nquasi-optimal error control.\n

Citations

• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems

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