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Article Dans Une Revue Advances in Computational Mathematics Année : 2020

Trefftz Discontinuous Galerkin basis functions for a class of Friedrichs systems coming from linear transport

Résumé

The Trefftz discontinuous Galerkin (TDG) method provides natural well-balanced (WB) and asymptotic preserving (AP) discretization since exact solutions are used locally in the basis functions. However, one difficult point may be the construction of such solutions which is a necessary first step in order to apply the TDG scheme. This works deals with the construction of solutions to Friedrichs systems with relaxation with application to the spherical harmonics approximation of the transport equation (the so-called PN models). Various exponential and polynomial solutions are constructed. Two numerical tests on the P3 model illustrate the good accuracy of the TDG method. They show that the exponential solutions lead to accurate schemes to capture boundary layers on a coarse mesh and that a combination of exponential and polynomial solutions is efficient in a regime with vanishing absorption coefficient.
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Dates et versions

hal-01964528 , version 1 (22-12-2018)

Identifiants

  • HAL Id : hal-01964528 , version 1

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Christophe Buet, Bruno Despres, Guillaume Morel. Trefftz Discontinuous Galerkin basis functions for a class of Friedrichs systems coming from linear transport. Advances in Computational Mathematics, 2020. ⟨hal-01964528⟩
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