Nodal Superconvergence of SDFEM for Singularly Perturbed Problems

In this paper, we analyze the streamline diffusion finite element method for one dimensional singularly perturbed convection-diffusion-reaction problems. Local error estimates on a subdomain where the solution is smooth are established. We prove that for a special group of exact solutions, the nodal error converges at a superconvergence rate of order (ln ε ⁻¹/N)^2k (or (ln N/N)^2k ) on a Shishkin mesh. Here ε is the singular perturbation parameter and 2N denotes the number of mesh elements. Numerical results illustrating the sharpness of our theoretical findings are displayed.