Nodal Superconvergence of SDFEM for Singularly Perturbed Problems
Mathematics and Natural Sciences
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.
Journal of Scientific Computing
(2012). Nodal Superconvergence of SDFEM for Singularly Perturbed Problems. Journal of Scientific Computing, 50(2), 405-433.
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