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

Hochbruck, Marlis; Sturm, Andreas

Abstract:
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 ineficient due to their strict CFL condition stemming from the fine grid elements. In the last years this issue of so-called grid-induced stifiness was successfully tackled with locally implicit time integrators. So far, these methods were limited to unstabilized (central uxes) dG methods. However, stabilized (upwind uxes) 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 using an upwind uxes dG discretization on the coarse part of the grid. The construction is based on a rigorous error analysis which shows that the stabilization operators have to be split differently than the Maxwell operator. Moreover, our earlier analysis of a central uxes locally implicit method based on semigroup theory applies but does not yield optimal convergence rates. In this paper we rigorously prove ... mehr


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2017
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000070153
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-701535
KITopen ID: 1000070153
Verlag KIT, Karlsruhe
Umfang 30 S.
Serie CRC 1173 ; 2017/12
Schlagworte locally implicit methods, time integration, energy techniques, upwind fluxes discontinuous Galerkin finite lements, error analysis, Maxwell’s equations
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