Abstract
A Galerkin finite element method that uses piecewise bilinears on a simple piecewise equidistant mesh is applied to a linear convection-dominated convection-diffusion problem in two dimensions. The method is shown to be convergent, uniformly in the perturbation parameter, of orderN−1lnNin a global energy norm and of orderN−1/2ln3/2Npointwise near the outflow boundary, where the total number of mesh points isO(N2).
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