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A unified error analysis for the numerical solution of nonlinear wave-type equations with application to kinetic boundary conditions

Leibold, Jan

Abstract:
In this thesis, a unified error analysis for discretizations of nonlinear first- and second-order wave-type equations is provided. For this, the wave equations as well as their space discretizations are considered as nonlinear evolution equations in Hilbert spaces. The space discretizations are supplemented with Runge-Kutta time discretizations. By employing stability properties of monotone operators, abstract error bounds for the space, time, and full discretizations are derived.

Further, for semilinear second-order wave-type equations, an implicit-explicit time integration scheme is presented. This scheme only requires the solution of a linear system of equations in each time step and it is stable under a step size restriction only depending on the nonlinearity. It is proven that the scheme converges with second order in time and in combination with the abstract space discretization of the unified error analysis, corresponding full discretization error bounds are derived.

The abstract results are used to derive convergence rates for an isoparametric finite element space discretization of a wave equation with kinetic boundary conditions and nonlinear forcing and damping terms. ... mehr

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Volltext §
DOI: 10.5445/IR/1000130222
Veröffentlicht am 10.03.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Hochschulschrift
Publikationsdatum 10.03.2021
Sprache Englisch
Identifikator KITopen-ID: 1000130222
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 107 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Angewandte und Numerische Mathematik (IANM)
Prüfungsdatum 24.02.2021
Referent/Betreuer Prof. M. Hochbruck
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Schlagwörter numerical analysis, nonlinear wave-type equations, nonlinear monotone operators, abstract error analysis, a priori error estimates, nonconforming space discretization, full discretization, implicit-explicit time integration, IMEX scheme, acoustic boundary conditions, dynamic boundary conditions
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