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Maximum norm error bounds for the full discretization of non-autonomous wave equations

Dörich, Benjamin ORCID iD icon; Leibold, Jan; Maier, Bernhard


In the present paper, we consider a specific class of non-autonomous wave equations on a smooth, bounded domain and their discretization in space by isoparametric finite elements and in time by the implicit Euler method. Building upon the work of Baker and Dougalis (1980), we prove maximum norm estimates for the semi discretization in space and the full discretization.
The key tool is the gain of integrability coming from the inverse of the discretized differential operator.
For this, we have to pay with time derivatives on the error in the $L^2$-norm which are reduced to estimates of the differentiated initial errors.

Volltext §
DOI: 10.5445/IR/1000141540
Veröffentlicht am 23.12.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 12.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000141540
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 31 S.
Serie CRC 1173 Preprint ; 2021/47
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter error analysis, full discretization, wave equation, maximum norm error bounds, nonconforming space discretization, isoparametric finite elements, a-priori error bounds
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