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On averaged exponential integrators for semilinear wave equations with solutions of low-regularity

Buchholz, Simone; Dörich, Benjamin; Hochbruck, Marlis

Abstract:
In this paper we introduce a class of second-order exponential schemes for the time integration of semilinear wave equations. They are constructed such that the established error bounds only depend on quantities obtained from a well-posedness result of a classical solution. To compensate missing regularity of the solution the proofs become considerably more involved compared to a standard error analysis. Key tools are appropriate filter functions as well as the integration-by-parts and summation-by-parts formulas. We include numerical examples to illustrate the advantage of the proposed methods.

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Volltext §
DOI: 10.5445/IR/1000117802
Veröffentlicht am 23.03.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000117802
Verlag KIT, Karlsruhe
Umfang 27 S.
Serie CRC 1173 ; 2020/8
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter highly oscillatory problems, error bounds, order-reduction, time-integration, second-order evolution equations, filter functions, summation-by-parts formula
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