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Error analysis for space and time discretizations of quasilinear wave-type equations

Maier, Bernhard

Abstract:
This thesis provides a unified framework for the error analysis for space and time discretizations of a quite general class of quasilinear wave-type problems.
For the space discretization we prove a rigorous error estimate based on semigroup theory for nonautonomous problems. Compared to previous results, which are mostly based on Banach’s fixed-point theorem, this approach allows for a better insight into the individual error contributions. Furthermore, since wellposedness results for quasilinear wave-type problems are in general based on severe regularity assumptions with respect to the boundary of the domain, we consider nonconforming space discretizations in order to allow for domain approximation.
Furthermore, we provide a rigorous error analysis for the full discretization with three different one-step time-integration schemes. On the one hand, we consider the implicit midpoint rule and a linearized version thereof. On the other hand, we also investigate the leapfrog scheme, which is an explicit scheme.
Throughout this thesis, we illustrate the relevance of the abstract framework by application of our results to the undamped Westervelt equation and the Maxwell equations with Kerr nonlinearity. ... mehr

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Volltext §
DOI: 10.5445/IR/1000120935
Veröffentlicht am 10.07.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Hochschulschrift
Publikationsdatum 10.07.2020
Sprache Englisch
Identifikator KITopen-ID: 1000120935
Verlag Karlsruhe
Umfang 148 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 27.05.2020
Referent/Betreuer Prof. M. Hochbruck
Schlagwörter numerical analysis, quasilinear wave-type equations, abstract error analysis, a priori error estimates, nonconforming space discretization, full discretization, implicit midpoint rule, leapfrog scheme, Westervelt equation, Maxwell equations, Kerr nonlinearity
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