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Robust fully discrete error bounds for the Kuznetsov equations in the inviscid limit

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

Abstract:

The Kuznetsov equation is a classical wave model of acoustics that incorpo- rates quadratic gradient nonlinearities. When its strong damping vanishes, it undergoes a singular behavior change, switching from a parabolic-like to a hyperbolic quasilinear evolution. In this work, we establish for the first time the optimal error bounds for its finite element approximation as well as a semi-implicit fully discrete approximation that are robust with respect to the vanishing damping parameter. The core of the new arguments lies in devising energy estimates directly for the error equation where one can more easily exploit the polynomial structure of the nonlinearities and compensate inverse estimates with smallness conditions on the error. Numerical experiments are included to illustrate the theoretical results.


Volltext §
DOI: 10.5445/IR/1000167217
Veröffentlicht am 12.01.2024
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 01.2024
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000167217
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 35 S.
Serie CRC 1173 Preprint ; 2024/1
Projektinformation SFB 1173/3 (DFG, DFG KOORD, SFB 1173/3)
Externe Relationen Forschungsdaten/Software
Siehe auch
Schlagwörter asymptotic-preserving error estimates, full discretization, Kuznetsov equation, nonlinear acoustics
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