On aposteriori error analysis of DG schemes approximating hyperbolic conservation laws

Jan Giesselmann; Tristan Pryer

doi:10.1007/978-3-319-05684-5_30

On aposteriori error analysis of DG schemes approximating hyperbolic conservation laws

Research output: Chapter or section in a book/report/conference proceeding › Chapter 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 language	English
Title of host publication	Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7
Editors	Christian Rohde, Jürgen Fuhrmann, Mario Ohlberger
Publisher	Springer New York
Pages	313-321
Number of pages	9
ISBN (Electronic)	9783319056838
DOIs	https://doi.org/10.1007/978-3-319-05684-5_30
Publication status	Published - 13 May 2014
Event	7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7 - Berlin, Germany Duration: 15 Jun 2014 → 20 Jun 2014

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	77
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7
Country/Territory	Germany
City	Berlin
Period	15/06/14 → 20/06/14

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2014.

ASJC Scopus subject areas

General Mathematics

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10.1007/978-3-319-05684-5_30

Cite this

Giesselmann, J., & Pryer, T. (2014). On aposteriori error analysis of DG schemes approximating hyperbolic conservation laws. In C. Rohde, J. Fuhrmann, & M. Ohlberger (Eds.), Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7 (pp. 313-321). (Springer Proceedings in Mathematics and Statistics; Vol. 77). Springer New York. https://doi.org/10.1007/978-3-319-05684-5_30

On aposteriori error analysis of DG schemes approximating hyperbolic conservation laws. / Giesselmann, Jan; Pryer, Tristan.
Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7. ed. / Christian Rohde; Jürgen Fuhrmann; Mario Ohlberger. Springer New York, 2014. p. 313-321 (Springer Proceedings in Mathematics and Statistics; Vol. 77).

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

Giesselmann, J & Pryer, T 2014, On aposteriori error analysis of DG schemes approximating hyperbolic conservation laws. in C Rohde, J Fuhrmann & M Ohlberger (eds), Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects, FVCA 7. Springer Proceedings in Mathematics and Statistics, vol. 77, Springer New York, pp. 313-321, 7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7, Berlin, Germany, 15/06/14. https://doi.org/10.1007/978-3-319-05684-5_30

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On aposteriori error analysis of DG schemes approximating hyperbolic conservation laws

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