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Convergence analysis of energy conserving explicit local time-stepping methods for the wave equation

Grote, Marcus J.; Mehlin, Michaela; Sauter, Stefan A.

Local adaptivity and mesh refinement are key to the efficient simulation of wave phenomena in heterogeneous media or complex geometry. Locally refined meshes, however, dictate a small time-step everywhere with a crippling effect on any explicit time-marching method. In [18] a leap-frog (LF) based explicit local time-stepping (LTS) method was proposed, which overcomes the severe bottleneck due to a few small elements by taking small time-steps in the locally refined region and larger steps elsewhere. Here optimal convergence rates are rigorously proved for the fully-discrete LTS-LF method when combined with a standard conforming finite element method (FEM) in space. Numerical results further illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of corner singularities.

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Volltext §
DOI: 10.5445/IR/1000075943
Veröffentlicht am 25.10.2017
Seitenaufrufe: 16
seit 04.05.2018
Downloads: 37
seit 25.10.2017
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000075943
Verlag KIT, Karlsruhe
Umfang 28 S.
Serie CRC 1173 ; 2017/27
Schlagworte wave propagation, finite element methods, explicit time integration, leap-frog method, error analysis, convergence theory
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