An analysis of a uniformly convergent finite difference/finite element scheme for a model singular-perturbation problem

Author:
Eugene C. Gartland

Journal:
Math. Comp. **51** (1988), 93-106

MSC:
Primary 65L10; Secondary 65L60

DOI:
https://doi.org/10.1090/S0025-5718-1988-0942145-6

MathSciNet review:
942145

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Abstract: Uniform convergence is proved for the El-Mistikawy-Werle discretization of the problem on (0,1), , , subject only to the conditions and . The principal tools used are a certain representation result for the solutions of such problems that is due to the author [*Math. Comp.*, v. 48, 1987, pp. 551-564] and the general stability results of Niederdrenk and Yserentant [*Numer. Math.*, v. 41, 1983, pp. 223-253]. Global uniform convergence is proved under slightly weaker assumptions for an equivalent Petrov-Galerkin formulation.

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0942145-6

Article copyright:
© Copyright 1988
American Mathematical Society