On aposteriori error analysis of DG schemes approximating hyperbolic conservation laws

Jan Giesselmann, Tristan Pryer

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

Abstract

This contribution is concerned with aposteriori error analysis of discontinuous Galerkin (dG) schemes approximating hyperbolic conservation laws. In the scalar case the aposteriori analysis is based on the L1contraction property and the doubling of variables technique. In the system case the appropriate stability framework is in L2, based on relative entropies. It is only applicable if one of the solutions, which are compared to each other, isLipschitz. FordGschemes approximating hyperbolic conservation laws neither the entropy solution nor the numerical solution need to be Lipschitz.We explain how this obstacle can be overcome using a reconstruction approach which leads to an aposteriori error estimate.

Original languageEnglish
Title of host publicationFinite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7
EditorsChristian Rohde, Jürgen Fuhrmann, Mario Ohlberger
PublisherSpringer New York
Pages313-321
Number of pages9
ISBN (Electronic)9783319056838
DOIs
Publication statusPublished - 13 May 2014
Event7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7 - Berlin, Germany
Duration: 15 Jun 201420 Jun 2014

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume77
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7
Country/TerritoryGermany
CityBerlin
Period15/06/1420/06/14

ASJC Scopus subject areas

  • Mathematics(all)

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