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A unified error analysis for nonlinear wave-type equations with application to acoustic boundary conditions

Leibold, Jan

Abstract:
In this work we present a unified error analysis for abstract space discretizations of nonlinear wave-type equations. This yields an error bound in terms of discretization and interpolation errors that can be applied to various equations and space discretizations fitting in the abstract setting. We use the unified error analysis to prove novel convergence rates for a non-conforming finite element space discretization of wave equations with nonlinear acoustic boundary conditions and illustrate the error bound by some numerical experiments.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 11.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000140080
Umfang 27 S.
Serie CRC 1173 Preprint ; 2021/44
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter nonlinear evolution equations, monotone operators, non-conforming space discretization, acoustic boundary conditions, dynamic boundary conditions, nonlinear wave equations, a-priori error analysis, finite element method
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