An analysis of a superconvergence result for a singularly perturbed boundary value problem

Authors:
Eugene O'Riordan and Martin Stynes

Journal:
Math. Comp. **46** (1986), 81-92

MSC:
Primary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1986-0815833-8

MathSciNet review:
815833

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Abstract: We give a new proof that the El-Mistikawy and Werle finite-difference scheme is uniformly second-order accurate for a nonselfadjoint singularly perturbed boundary value problem. To do this, we use exponential finite elements and a discretized Green's function. The proof is direct, gives the nodal errors explicitly in integral form, and involves much less computation than in previous proofs of the result.

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0815833-8

Article copyright:
© Copyright 1986
American Mathematical Society