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Mathematics of Computation

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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
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 $ {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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Article copyright: © Copyright 1991 American Mathematical Society