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

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- by Eugene O’Riordan and Martin Stynes PDF
- Math. Comp.
**47**(1986), 555-570 Request permission

## 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 $C{h^2}$, 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 ${L^\infty }[0,1]$.

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## Additional Information

- © Copyright 1986 American Mathematical Society
- Journal: Math. Comp.
**47**(1986), 555-570 - MSC: Primary 65L10
- DOI: https://doi.org/10.1090/S0025-5718-1986-0856702-7
- MathSciNet review: 856702