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An implicit-explicit time discretization scheme for second-order semilinear wave equations with application to dynamic boundary conditions

Hochbruck, Marlis; Leibold, Jan

We construct and analyze a second-order implicit-explicit (IMEX) scheme for the time integration of semilinear second-order wave equations. The scheme treats the stiff linear part of the problem implicitly and the nonlinear part explicitly. This makes the scheme unconditionally stable and at the same time very efficient, since it only requires the solution of one linear system of equations per time step.
For the combination of the IMEX scheme with a general, abstract, nonconforming space discretization we prove a full discretization error bound. We then apply the method to a nonconforming finite element discretization of an acoustic wave equation with a kinetic boundary condition. This yields a fully discrete scheme and a corresponding a-priori error estimate.

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Volltext §
DOI: 10.5445/IR/1000122353
Veröffentlicht am 04.08.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsdatum 27.07.2020
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000122353
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 24 S.
Serie CRC 1173 Preprint ; 2020/20
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter implicit-explicit time integration, IMEX, dynamic boundary conditions, semilinear wave equation, nonconforming space discretization, error analysis, a-priori error bounds, semilinear evolution equations, operator semigroups
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