ANALYSIS OF THE SPACE SEMI-DISCRETIZED SUPG METHOD FOR TRANSIENT CONVECTION-DIFFUSION EQUATIONS

We consider space semi-discretization of the transient convection-diffusion equation using a Streamline Upwind Petrov-Galerkin (SUPG) finite element method. We show stability and convergence both for the standard SUPG formulation with elementwise evaluated Laplacian and for a weakly consistent formulation where the elementwise Laplacian is replaced by a discrete, reconstructed, Laplacian. Some numerical examples are presented to illustrate the theory.