The use of classical Lax-Friedrichs Riemann solvers with discontinuous Galerkin methods
While conducting a von Neumann stability analysis of discontinuous Galerkin methods we discovered that the classic Lax-Friedrichs Riemann solver is unstable for all time-step sizes. We describe a simple modification of the Riemann solver's dissipation returns the method to stability. Furthermore, the method has a smaller truncation error than the corresponding method with an upwind flux for the RK2-DG(1) method. These results are verified upon testing. Copyright (C) 2002 John Wiley Sons, Ltd.
lax-friedrichs discontinuous galerkin von neumann stability analysis