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Trigonometric integrators for quasilinear wave equations

Gauckler, Ludwig; Lu, Jianfeng; Marzuola, Jeremy L.; Rousset, Frédéric; Schratz, Katharina

Trigonometric time integrators are introduced as a class of explicit numerical methods for quasilinear wave equations. Second-order convergence for the semi-discretization in time with these integrators is shown for a sufficiently regular exact solution. The time integrators are also combined with a Fourier spectral method into a fully discrete scheme, for which error bounds are provided without requiring any CFL-type coupling of the discretization parameters. The proofs of the error bounds are based on energy techniques and on the semiclassical Gårding inequality.

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DOI: 10.5445/IR/1000088928
Veröffentlicht am 21.12.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000088928
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 36 S.
Serie CRC 1173 ; 2018/50
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagwörter quasilinear wave equation, trigonometric integrators, exponential integrators, error bounds, loss of derivatives, energy estimates
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