Convergence Analysis of Energy Conserving

Grote, Marcus J. and Mehlin, Michaela and Sauter, Stefan A.. (2018) Convergence Analysis of Energy Conserving. SIAM Journal on Numerical Analysis, 56 (2). pp. 994-1021.

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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)
UniBasel Contributors:Grote, Marcus J.
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Society for Industrial and Applied Mathematics
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:06 Aug 2020 06:40
Deposited On:05 Aug 2020 16:06

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