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

页码：521 / 557

页数：37