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Space-time discontinuous Galerkin discretizations for linear first-order hyperbolic evolution systems. Revised March 2016

Dörfler, Willy; 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.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000053080
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-530800
KITopen ID: 1000053080
Verlag KIT, Karlsruhe
Umfang 21 S.
Serie CRC 1173 ; 2015/4,revised
Schlagworte Space-time methods, discontinuous Galerkin finite elements, linear hyperbolic systems, transport equation, wave equation, Maxwell's equations
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