Kopriva, David A., Gassner, Gregor J. and Nordstrom, Jan ORCID: 0000-0002-7972-6183 (2021). Stability of Discontinuous Galerkin Spectral Element Schemes for Wave Propagation when the Coefficient Matrices have Jumps. J. Sci. Comput., 88 (1). NEW YORK: SPRINGER/PLENUM PUBLISHERS. ISSN 1573-7691
Full text not available from this repository.Abstract
We use the behavior of the L-2 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 L-2 norm is not bounded in terms of the initial data for homogeneous and dissipative boundary conditions for such systems, the L-2 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 L-2 norm, plus an added dissipation that depends on how much the approximate solution fails to satisfy the Rankine-Hugoniot jump.
Item Type: | Journal Article | ||||||||||||||||
Creators: |
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URN: | urn:nbn:de:hbz:38-593887 | ||||||||||||||||
DOI: | 10.1007/s10915-021-01516-w | ||||||||||||||||
Journal or Publication Title: | J. Sci. Comput. | ||||||||||||||||
Volume: | 88 | ||||||||||||||||
Number: | 1 | ||||||||||||||||
Date: | 2021 | ||||||||||||||||
Publisher: | SPRINGER/PLENUM PUBLISHERS | ||||||||||||||||
Place of Publication: | NEW YORK | ||||||||||||||||
ISSN: | 1573-7691 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
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URI: | http://kups.ub.uni-koeln.de/id/eprint/59388 |
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