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2. Parallel adaptive discontinuous Galerkin discretizations in space and time for linear elastic and acoustic waves

From the book Space-Time Methods

Willy Dörfler , Stefan Findeisen , Christian Wieners and Daniel Ziegler

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.

© 2019 Walter de Gruyter GmbH, Berlin/Munich/Boston
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