Trefftz Discontinuous Galerkin Method for Friedrichs Systems with Linear Relaxation: Application to the P1 Model

被引：8
|
作者：
Morel, Guillaume [1 ,2 ]
Buet, Christophe [1 ]
Despres, Bruno [2 ,3 ]
机构：
[1] CEA, DAM, DIF, F-91297 Arpajon, France
[2] Univ Pierre & Marie Curie Paris VI, Lab Jacques Louis Lions, UMR 7598, F-75005 Paris, France
[3] Inst Univ France, Paris, France
来源：
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS | 2018年 / 18卷 / 03期
关键词：
Trefftz Methods; Discontinuous Galerkin Method; Asymptotic-Preserving and Well-Balanced Scheme; Stiff Relaxation; P1; System; WEAK VARIATIONAL FORMULATION; FINITE-ELEMENT-METHOD; PLANE-WAVES; NUMERICAL-METHOD; TRANSPORT; EQUATION; SCHEMES;
D O I：
10.1515/cmam-2018-0006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This work deals with the first Trefftz Discontinuous Galerkin (TDG) scheme for a model problem of transport with relaxation. The model problem is written as a P-N or S-N model, and we study in more details the P-1 model in dimension 1 and 2. We show that the TDG method provides naturalwell-balanced and asymptotic preserving discretization since exact solutions are used locally in the basis functions. High-order convergence with respect to the mesh size in two dimensions is proved together with the asymptotic property for P-1 model in dimension one. Numerical results in dimensions 1 and 2 illustrate the theoretical properties.
引用
收藏
页码：521 / 557
页数：37
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