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

Giesselmann, J., Makridakis, C. and Pryer, T. (2015) A Posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws. SIAM Journal on Numerical Analysis (SINUM), 53 (3). pp. 1280-1303. ISSN 0036-1429 doi: 10.1137/140970999

Abstract/Summary

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete 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, which leads to error control in the case of smooth solutions. 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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/40916
Identification Number/DOI	10.1137/140970999
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Society for Industrial and Applied Mathematics
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