Efficient high-order time discretization methods for PDEs

May 11-13, 2022 - Villa Orlandi, Anacapri, Italy

Contributed Talk

Implicit multi-derivative time discretization for the DG method

Jochen Schütz,

UHasselt University, Belgium

Abstract

In this talk, we present recent results on how to efficiently combine a discontinuous Galerkin method with a deferred correction multi-derivative time discretization. We show how to augment the spatial operator in such a way that the fully discrete scheme is stable; this ultimately results in an extended system matrix. We investigate and develop preconditioners for this extended matrix and show how to efficiently solve the resulting non-linear algebraic equations using a state-of-the-art Jacobian-free Newton-Krylov approach. Finally, numerical results for the compressible Navier-Stokes equation are shown.


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