A posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws

Jan Giesselmann, Charalambos Makridakis, Tristan Pryer

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Abstract

In this work we construct reliable a posteriori estimates for some discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator.
Original languageEnglish
Pages (from-to)1280-1303
Number of pages24
JournalSIAM Journal on Numerical Analysis
Volume53
Issue number3
Early online date19 May 2015
DOIs
Publication statusPublished - 2015

Keywords

  • math.NA

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