The semi-discrete streamline diffusion finite element method for time-dependented convection-diffusion problems

In this paper, a semi-discrete streamline diffusion finite element method (SDFEM) for solving the time-dependent convection-dominated diffusion problem in one dimension is studied. Under the mild regularity assumptions, the convergence/stability results are derived. Finally, some numerical experiments are given for a convection-dominated problem with boundary layer at x=1 by using P1-element. Compared with the finite difference streamline diffusion method (FDSDM), the semi-discrete SDFEM is more stable and it can imitate the exact solution effectively.