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A posteriori analysis of discontinuous galerkin schemes for systems of hyperbolic conservation laws
journal contribution
posted on 2023-06-08, 22:37 authored by Jan Giesselmann, Charalambos MakridakisCharalambos Makridakis, Tristan PryerIn 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.
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- Published
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- Published version
Journal
SIAM Journal on Numerical AnalysisISSN
0036-1429Publisher
Society for Industrial and Applied MathematicsExternal DOI
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3Volume
53Page range
1280-1303Department affiliated with
- Mathematics Publications
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- Yes
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- Yes
Legacy Posted Date
2015-09-28First Open Access (FOA) Date
2015-09-28First Compliant Deposit (FCD) Date
2015-09-28Usage metrics
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