A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions

Authors:
Eugene O’Riordan and Martin Stynes

Journal:
Math. Comp. **57** (1991), 47-62

MSC:
Primary 65N30; Secondary 35B25, 35B45

DOI:
https://doi.org/10.1090/S0025-5718-1991-1079029-1

MathSciNet review:
1079029

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Abstract: We analyze a new Galerkin finite element method for numerically solving a linear convection-dominated convection-diffusion problem in two dimensions. The method is shown to be convergent, uniformly in the perturbation parameter, of order in a global energy norm which is stronger than the norm. This order is optimal in this norm for our choice of trial functions.

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DOI:
https://doi.org/10.1090/S0025-5718-1991-1079029-1

Article copyright:
© Copyright 1991
American Mathematical Society