Trefftz Discontinuous Galerkin Method for Friedrichs Systems with Linear Relaxation: Application to the P 1 Model

Abstract

Abstract 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 {P_{N}} or S N {S_{N}} model, and we study in more details the P 1 {P_{1}} model in dimension 1 and 2. We show that the TDG method provides natural well-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 {P_{1}} model in dimension one. Numerical results in dimensions 1 and 2 illustrate the theoretical properties.