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

Buchholz, Simone; Dörich, Benjamin ORCID iD icon; 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.


Verlagsausgabe §
DOI: 10.5445/IR/1000137858
Veröffentlicht am 23.09.2021
Originalveröffentlichung
DOI: 10.1007/s42985-020-00045-9
Dimensions
Zitationen: 1
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 04.2021
Sprache Englisch
Identifikator ISSN: 2662-2963, 2662-2971
KITopen-ID: 1000137858
Erschienen in SN Partial Differential Equations and Applications
Verlag Springer Science and Business Media
Band 2
Heft 2
Seiten Art.-Nr.: 23
Vorab online veröffentlicht am 09.03.2021
Nachgewiesen in Dimensions
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