KIT | KIT-Bibliothek | Impressum | Datenschutz

Space-time discontinuous Galerkin methods for weak solutions of hyperbolic linear symmetric Friedrichs systems

Corallo, Daniele 1; Dörfler, Willy ORCID iD icon 1; Wieners, Christian 1
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract:

We study weak solutions and its approximation of hyperbolic linear symmetric Friedrichs systems describing acoustic, elastic, or electro-magnetic waves. For the corresponding first-order systems we construct discontinuous Galerkin discretizations in space and time with full upwind, and we show primal and dual consistency. Stability and convergence estimates are provided with respect to a mesh-dependent DG norm which includes the $L_2$ norm at final time. Numerical experiments confirm that the a piori results are of optimal order also for solutions with low regularity, and we show that the error in the DG norm can be closely approximated with a residual-type error indicator.


Volltext §
DOI: 10.5445/IR/1000149977
Veröffentlicht am 16.08.2022
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 08.2022
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000149977
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 22 S.
Serie CRC 1173 Preprint ; 2022/36
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Abstract/Volltext
Schlagwörter weak solution of linear symmetric Friedrichs systems, discontinuous Galerkin methods in space and time, error, estimators for first-order systems
Relationen in KITopen
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
KITopen Landing Page