2. Parallel adaptive discontinuous Galerkin discretizations in space and time for linear elastic and acoustic waves
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Willy Dörfler
Abstract
We introduce a space-time discretization for elastic and acoustic waves using a discontinuous Galerkin approximation in space, and a Petrov-Galerkin scheme in time. For the DG method, the upwind flux is evaluated by explicitly solving a Riemann problem. Then we show well-posedness and convergence of the discrete system. Based on goal-oriented dual-weighted error estimation, an adaptive strategy is introduced. The full space-time linear system is solved with a parallel multilevel preconditioner. Numerical experiments for acoustic and elastic waves underline the efficiency of the overall adaptive solution process.
Abstract
We introduce a space-time discretization for elastic and acoustic waves using a discontinuous Galerkin approximation in space, and a Petrov-Galerkin scheme in time. For the DG method, the upwind flux is evaluated by explicitly solving a Riemann problem. Then we show well-posedness and convergence of the discrete system. Based on goal-oriented dual-weighted error estimation, an adaptive strategy is introduced. The full space-time linear system is solved with a parallel multilevel preconditioner. Numerical experiments for acoustic and elastic waves underline the efficiency of the overall adaptive solution process.
Chapters in this book
- Frontmatter I
- Preface V
- Contents IX
- 1. Space-time boundary element methods for the heat equation 1
- 2. Parallel adaptive discontinuous Galerkin discretizations in space and time for linear elastic and acoustic waves 61
- 3. A space-time discontinuous Petrov–Galerkin method for acoustic waves 89
- 4. A space-time DPG method for the wave equation in multiple dimensions 117
- 5. Adaptive space-time isogeometric analysis for parabolic evolution problems 141
- 6. Generating admissible space-time meshes for moving domains in (d + 1) dimensions 185
- 7. Space-time finite element methods for parabolic evolution equations: discretization, a posteriori error estimation, adaptivity and solution 207
- Index 249
- Radon Series on Computational and Applied Mathematics 251
Chapters in this book
- Frontmatter I
- Preface V
- Contents IX
- 1. Space-time boundary element methods for the heat equation 1
- 2. Parallel adaptive discontinuous Galerkin discretizations in space and time for linear elastic and acoustic waves 61
- 3. A space-time discontinuous Petrov–Galerkin method for acoustic waves 89
- 4. A space-time DPG method for the wave equation in multiple dimensions 117
- 5. Adaptive space-time isogeometric analysis for parabolic evolution problems 141
- 6. Generating admissible space-time meshes for moving domains in (d + 1) dimensions 185
- 7. Space-time finite element methods for parabolic evolution equations: discretization, a posteriori error estimation, adaptivity and solution 207
- Index 249
- Radon Series on Computational and Applied Mathematics 251
