Fourier Analysis of DG Schemes for Advection‐Diffusion

Abstract

This work compares the wave propagation properties of discontinuous Galerkin (DG) schemes for advection-diffusion problems in particular with respect to the discretization of diffusion terms. Extending previous investigations, the advection discretization now additionally varies between the choices of central or upwind fluxes. The results show that a previously recognized better performance of central schemes for well-resolved problems only hold for even polynomial degrees and that upwind-type discretizations also perform better on Gauss-Lobatto nodes.