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Space-time discontinuous Galerkin discretizations for linear first-order hyperbolic evolution systems

Dörfler, Willy ORCID iD icon; Findeisen, Stefan; Wieners, Christian

Abstract:

We introduce a space-time discretization for linear first-order hyperbolic evolution systems using a discontinuous Galerkin approximation in space and a Petrov-Galerkin scheme in time. We show well-posedness and convergence of the discrete system. Then we introduce an adaptive strategy based on goal-oriented dual-weighted error estimation. The full space-time linear system is solved with a parallel multilevel preconditioner. Numerical experiments for the linear transport equation and the Maxwell equation in 2D underline the effciency of the overall adaptive solution process.


Volltext §
DOI: 10.5445/IR/1000050018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2015
Sprache Englisch
Identifikator ISSN: 2365-662X
urn:nbn:de:swb:90-500185
KITopen-ID: 1000050018
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 22 S.
Serie CRC 1173 ; 2015/4
Schlagwörter Space-time methods, discontinuous Galerkin finite elements, linear hyperbolic systems, transport equation, wave equation, Maxwell's equations
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