A uniformly accurate finite-element method for a singularly perturbed one-dimensional reaction-diffusion problem

Authors:
Eugene O'Riordan and Martin Stynes

Journal:
Math. Comp. **47** (1986), 555-570

MSC:
Primary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856702-7

MathSciNet review:
856702

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Abstract: A finite-element method with exponential basis elements is applied to a selfadjoint, singularly perturbed, two-point boundary value problem. The tridiagonal difference scheme generated is shown to be uniformly second-order accurate for this problem (i.e., the nodal errors are bounded by , where *C* is independent of the mesh size *h* and the perturbation parameter). With a certain choice of trial functions, uniform first-order accuracy is obtained in .

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0856702-7

Article copyright:
© Copyright 1986
American Mathematical Society