A Streamline-Upwind-Full-Galerkin Method for Space-Time Convection Dominated Transport Problems

An original space-time finite element approach for the solution of the diffusion-convection equation is proposed in this paper. A slight manipulation of the differential equation suggests that transient transport problems may in fact be seen as 'steady-state space-time transport problems', accurately and easily soluble by the standard Galerkin technique. However, concerning convective transport involving sharp fronts or coarse discretization, it is shown that implementation of dissipation along space-time trajectories significantly improves the solutions. Classical comparative test problems are run to establish the performances of this method, and to show the limits of the more sophisticated Petrov and Taylor-Galerkin schemes. Evocation of a possible space-time anisotropy generated by usual finite difference time-stepping procedures, as well as comparative analysis of amplification matrices, help to understand the accuracy and the robustness of the proposed approach.