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Error analysis for space discretizations of quasilinear wave-type equations

Hochbruck, Marlis; Maier, Bernhard

Abstract:
In this paper we study space discretizations of a general class of first- and second-order quasilinear wave-type problems. We present a rigorous error analysis based on a combination of inverse estimates with semigroup theory for nonautonomous linear Cauchy problems. Moreover, we provide refined results for the special case that the nonlinearities are local in space. As applications of these general results we derive novel error estimates for two prominent examples from nonlinear physics: the Westervelt equation and the Maxwell equations with Kerr nonlinearity. We conclude with a numerical example to illustrate our theoretical findings.

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Volltext §
DOI: 10.5445/IR/1000128952
Veröffentlicht am 26.01.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 01.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000128952
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 21 S.
Serie CRC 1173 Preprint ; 2021/2
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter quasilinear wave-type equations, abstract error analysis, a priori error estimates, Westervelt equation, Maxwell equations, Kerr nonlinearity
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