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

Jan Giesselmann; Charalambos Makridakis; Tristan Pryer

doi:10.1137/140970999

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

Jan Giesselmann, Charalambos Makridakis, Tristan Pryer

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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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 language	English
Pages (from-to)	1280-1303
Number of pages	24
Journal	SIAM Journal on Numerical Analysis
Volume	53
Issue number	3
Early online date	19 May 2015
DOIs	https://doi.org/10.1137/140970999
Publication status	Published - 2015

Keywords

math.NA

Access to Document

10.1137/140970999

1405.7616v1.PDF
(C) 2015 Society for Industrial and Applied Mathematics
Accepted author manuscript, 296 KB

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Tristan Pryer
- tmp38@bath.ac.uk
- Department of Mathematical Sciences - Reader
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Cite this

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