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Error analysis of a fully discrete discontinuous Galerkin alternating direction implicit discretization of a class of linear wave-type problems

Hochbruck, Marlis; Köhler, Jonas

Abstract:
This paper is concerned with the rigorous error analysis of a fully discrete scheme obtained by using a central fluxes discontinuous Galerkin (dG) method in space and the Peaceman–Rachford splitting scheme in time. We apply the scheme to a general class of wave-type problems and show that the resulting approximations as well as discrete derivatives thereof satisfy error bounds of the order of the polynomial degree used in the dG discretization and order two in time. In particular, the class of problems considered includes, e.g., the advection equation, the acoustic wave equation, and the Maxwell equations for which a very efficient implementation is possible via an alternating direction implicit (ADI) splitting.

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Volltext §
DOI: 10.5445/IR/1000127911
Veröffentlicht am 21.12.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 12.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000127911
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 33 S.
Serie CRC 1173 Preprint ; 2020/39
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter wave-type problems, time-integration, unconditionally stable, alternating direction implicit, ADI, discontinuous Galerkin, dG, rigorous error analysis, semigroup techniques, discrete derivatives, strong error bounds
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