Universität zu Köln

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.

Preview

PDF CDS_TR-2020-11.pdf Download (2MB) | Preview

Abstract

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)
Creators:	Creators Email ORCID ORCID Put Code Kopriva, David A. kopriva@math.fsu.edu UNSPECIFIED UNSPECIFIED Gassner, Gregor J. ggassner@math.uni-koeln.de orcid.org/0000-0002-1752-1158 UNSPECIFIED Nordström, Jan UNSPECIFIED UNSPECIFIED UNSPECIFIED
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 Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language Discontinuous Galerkin spectral element English stability English linear advection English discontinuous coefficients English
Refereed:	No
URI:	http://kups.ub.uni-koeln.de/id/eprint/29556