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Error analysis for full discretizations of quasilinear wave-type equations with two variants of the implicit midpoint rule

Maier, Bernhard

Abstract:

We study the full discretization of a general class of first- and second-order quasilinear wave-type problems with the implicit midpoint rule and a linearized variant thereof. Based on a proof by induction, we prove wellposedness and a rigorous error estimate for both schemes, combining energy techniques, inverse estimates, and a linearized fixed-point iteration for the analysis of the nonlinear scheme. To confirm the relevance of the general framework, we derive novel error esitmates for the full discretization of two prominent examples from nonlinear physics: the Westervelt equation and the Maxwell equations with Kerr nonlinearity.


Volltext §
DOI: 10.5445/IR/1000133244
Veröffentlicht am 21.05.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 05.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000133244
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 26 S.
Serie CRC 1173 Preprint ; 2021/24
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter quasilinear wave-type equations, abstract error analysis, full discretization, a priori error estimates, Westervelt equation, Maxwell equations, Kerr nonlinearity, implicit midpoint rule
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