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

O’Riordan, Eugene; Stynes, Martin

doi:10.1090/S0025-5718-1991-1079029-1

A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions
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by Eugene O’Riordan and Martin Stynes PDF

Math. Comp. 57 (1991), 47-62 Request permission

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 ${h^{1/2}}$ in a global energy norm which is stronger than the ${L^2}$ norm. This order is optimal in this norm for our choice of trial functions.

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