L∞ (L2)-error estimates for the DGFEM applied to convection–diffusion problems on nonconforming meshes

M. Feistauer; V. Dolejší; V. Kučera; V. Sobotíková

doi:10.1515/JNUM.2009.004

Published by De Gruyter June 16, 2009

L^∞ (L²)-error estimates for the DGFEM applied to convection–diffusion problems on nonconforming meshes

M. Feistauer , V. Dolejší , V. Kučera and V. Sobotíková

From the journal Journal of Numerical Mathematics

https://doi.org/10.1515/JNUM.2009.004

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Abstract

This paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection–diffusion Dirichlet problem. General nonconforming simplicial meshes are considered and the SIPG scheme is used. Under the assumption that the exact solution is sufficiently regular an L^∞ (L²)-optimal error estimate is derived. The theoretical results are illustrated by numerical experiments.

Keywords:: nonlinear convection–diffusion equation; discontinuous Galerkin finite element method; nonconforming meshes; hanging nodes and edges; symmetric formulation of diffusion terms; interior and boundary penalty; method of lines; optimal error estimates; experimental order of convergence

Published Online: 2009-06-16

Published in Print: 2009-June

L^∞ (L²)-error estimates for the DGFEM applied to convection–diffusion problems on nonconforming meshes

Abstract

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