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

Grote, Marcus and Mehlin, Michaela and Sauter, Stefan A.. (2017) Convergence analysis of energy conserving explicit local time-stepping methods for the wave equation. Preprints Fachbereich Mathematik, 2017 (02).

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Abstract

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 a rigorous convergence proof is presented 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.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Grote, Marcus J.
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:20 Apr 2019 15:10
Deposited On:28 Mar 2019 09:51

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