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Upwind discontinuous Galerkin space discretization and locally implicit time integration for linear Maxwell's equations

Hochbruck, Marlis; Sturm, Andreas

This paper is dedicated to the full discretization of linear Maxwell's equations, where the space discretization is carried out with a discontinuous Galerkin (dG) method on a locally refined spatial grid. For such problems explicit time integrators are inffcient due to their strict CFL condition stemming from the fine mesh elements in the spatial grid. In the last years this issue of so-called grid-induced stiffness was successfully tackled with locally implicit time integrators. So far, these methods were limited to unstabilized (central fluxes) dG methods. However, stabilized (upwind fluxes) dG schemes provide many benefits and thus are a popular choice in applications. In this paper we construct a new variant of a locally implicit time integrator based on an upwind fluxes dG discretization on the coarse part of the grid. In contrast to our earlier analysis of a central fluxes locally implicit method, we now use an energy technique to rigorously prove its stability and provide error bounds with optimal rates in space and time.

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Volltext §
DOI: 10.5445/IR/1000067269
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000067269
Verlag KIT, Karlsruhe
Umfang 30 S.
Serie CRC 1173 ; 2017/4
Schlagwörter locally implicit methods, time integration, finite elements, upwind fluxes discontinuous Galerkin, error analysis, energy techniques, Maxwell’s equations
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