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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

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To link to this item 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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:40916
Publisher:Society for Industrial and Applied Mathematics

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