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An explicit high order accurate predictor-corrector time integration method with consistent local time-stepping for discontinuous Galerkin schemes. (English) Zbl 1182.65145

Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics, Rethymno, Crete, Greece, September 18–22, 2009. Vol. 2. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0708-4/hbk; 978-0-7354-0709-1/set). AIP Conference Proceedings 1168, 2, 1188-1191 (2009).
Summary: A new explicit discretization for the time integration of the semi discrete discontinuous Galerkin (DG) scheme is presented. The time integration is based on a predictor-corrector approach, where the predictor is the solution of the so-called predictor ordinary differential equations (ODEs), which are simplified versions of the DG ODEs. For the time integration of the predictor ODEs a continuous extension Runge-Kutta scheme is used. The class of schemes shares the property that an analytically, polynomial time solution is available. This analytical time polynomial and the fact that the DG discretization only couples direct neighbor grid cells allows the adoption of a local time stepping algorithm. Despite the local time steps the fully discrete scheme is high order accurate in time, fully conservative and ideally suited for massively parallel computations, allowing an efficient discretization of large scale time dependent problems.
For the entire collection see [Zbl 1177.00116].

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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