Nodal Superconvergence of SDFEM for Singularly Perturbed Problems

Document Type

Article

Publication Date

2-1-2012

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

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.

Publication Title

Journal of Scientific Computing

Volume

50

Issue

2

First Page

405

Last Page

433

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