On the discontinuous Galerkin method for the numerical solution of the Navier-Stokes equations

The paper deals with the use of the discontinuous Galerkin finite element method (DGFEM) for the numerical solution of viscous compressible flows. We start with a scalar convection-diffusion equation and present a discretization with the aid of the non-symmetric variant of DGFEM with interior and boundary penalty terms. We also mention some theoretical results. Then we extend the scheme to the system of the Navier-Stokes equations and discuss the treatment of stabilization terms. Several numerical examples are presented. Copyright (C) 2004 John Wiley Sons, Ltd.