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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
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 $ 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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DOI: https://doi.org/10.1090/S0025-5718-1986-0856702-7
Article copyright: © Copyright 1986 American Mathematical Society