Name
Title | ||
|---|---|---|
Convergence Analysis of Energy Conserving Explicit Local Time-Stepping Methods for the Wave Equation. |
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 [J. Diaz and M. J. Grote, SIAM J. Sci. Comput., 31 (2009), pp. 1985-2014] 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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M1121925 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
wave propagation,finite element methods,explicit time integration,leap-frog method,error analysis,convergence theory | Convergence (routing),Mathematical optimization,Polygon mesh,Wave propagation,Mathematical analysis,Galerkin method,Finite element method,Complex geometry,Gravitational singularity,Wave equation,Mathematics | Journal |
Volume | Issue | ISSN |
56 | 2 | 0036-1429 |
Citations | PageRank | References |
1 | 0.36 | 15 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marcus J. Grote | 1 | 401 | 51.61 |
| Michaela Mehlin | 2 | 2 | 0.72 |
| S. A. Sauter | 3 | 138 | 38.87 |