CFL Condition and Boundary Conditions for DGM Approximation of Convection-Diffusion

Abstract. We propose a general method for the design of Discontinuous Galerkin Methods for non stationary linear equations. The method is based on a particular splitting of the bilinear forms that appear in the weak Discontinuous Galerkin Method. We prove that an appropriate time splitting gives a stable scheme whatever the order of the polynomial approximation . Various problems can be addressed with the same method. Numerical results are presented.