Palindromic discontinuous Galerkin method. (English) Zbl 1365.76251

Cancès, Clément (ed.) et al., Finite volumes for complex applications VIII – hyperbolic, elliptic and parabolic problems. FVCA 8, Lille, France, June 12–16, 2017. Cham: Springer (ISBN 978-3-319-57393-9/hbk; 978-3-319-57394-6/ebook; 978-3-319-58818-6/set). Springer Proceedings in Mathematics & Statistics 200, 171-178 (2017).
Summary: We present a high-order scheme for approximating kinetic equations with stiff relaxation. The construction is based on a high-order, implicit, upwind Discontinuous Galerkin formulation of the transport equations. In practice, because of the triangular structure of the implicit system, the computations are explicit. High order in time is achieved thanks to a palindromic composition method. The whole method is asymptotic-preserving with respect to the stiff relaxation and remains stable even with large CFL numbers.
For the entire collection see [Zbl 1371.65001].


76M28 Particle methods and lattice-gas methods
65L04 Numerical methods for stiff equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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