Kopriva, David A., Gassner, Gregor J. ORCID: 0000-0002-1752-1158 and Nordström, Jan (2020). Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps. Technical Report.


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We use the behavior of the L2 norm of the solutions of linear hyperbolic equations with discontinuous coefficient matrices as a surrogate to infer stability of discontinuous Galerkin spectral element methods (DGSEM). Although the L2 norm is not bounded by the initial data for homogeneous and dissipative boundary conditions for such systems, the L2 norm is easier to work with than a norm that discounts growth due to the discontinuities. We show that the DGSEM with an upwind numerical flux that satisfies the Rankine-Hugoniot (or conservation) condition has the same energy bound as the partial differential equation does in the L2 norm, plus an added dissipation that depends on how much the approximate solution fails to satisfy the Rankine-Hugoniot jump.

Item Type: Preprints, Working Papers or Reports (Technical Report)
CreatorsEmailORCIDORCID Put Code
Kopriva, David A.kopriva@math.fsu.eduUNSPECIFIEDUNSPECIFIED
Gassner, Gregor J.ggassner@math.uni-koeln.deorcid.org/0000-0002-1752-1158UNSPECIFIED
URN: urn:nbn:de:hbz:38-295561
Series Name at the University of Cologne: Technical report series. Center for Data and Simulation Science
Volume: 2020,11
Date: 26 November 2020
Language: English
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects: Natural sciences and mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
Discontinuous Galerkin spectral elementEnglish
linear advectionEnglish
discontinuous coefficientsEnglish
Refereed: No
URI: http://kups.ub.uni-koeln.de/id/eprint/29556


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