Universität zu Köln

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

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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:	Creators Email ORCID ORCID Put Code Kopriva, David A. UNSPECIFIED UNSPECIFIED UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Nordstrom, Jan UNSPECIFIED orcid.org/0000-0002-7972-6183 UNSPECIFIED
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
Uncontrolled Keywords:	Keywords Language FINITE-DIFFERENCE Multiple languages Mathematics, Applied Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/59388