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Strong Norm Error Bounds for Quasilinear Wave Equations Under Weak CFL-Type Conditions

Dörich, Benjamin ORCID iD icon 1
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract:

In the present paper, we consider a class of quasilinear wave equations on a smooth, bounded domain. We discretize it in space with isoparametric finite elements and apply a semi-implicit Euler and midpoint rule as well as the exponential Euler and midpoint rule to obtain four fully discrete schemes. We derive rigorous error bounds of optimal order for the semi-discretization in space and the fully discrete methods in norms which are stronger than the classical $H^1 \times L^2$ energy norm under weak CFL-type conditions. To confirm our theoretical findings, we also present numerical experiments.


Verlagsausgabe §
DOI: 10.5445/IR/1000168974
Veröffentlicht am 01.03.2024
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2024
Sprache Englisch
Identifikator ISSN: 1615-3375, 1615-3383
KITopen-ID: 1000168974
Erschienen in Foundations of Computational Mathematics
Verlag Springer-Verlag
Vorab online veröffentlicht am 13.02.2024
Schlagwörter Error analysis, Full discretization, Quasilinear wave equation, Nonconforming space discretization, Isoparametric finite elements, A-priori error bounds
Nachgewiesen in Dimensions
Scopus
Web of Science
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