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A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem. (English) Zbl 0917.65088
Two results on convergence uniform in the singular perturbation parameter are given for a singularly perturbed linear elliptic boundary value problem in two dimensions. Their error bounds are of order (i) $$(\ln N/N)$$ in a global energy norm and (ii) $$(\ln N)^{3/2}/\sqrt N$$ pointwise near the outflow boundary.

##### MSC:
 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35B25 Singular perturbations in context of PDEs 35J25 Boundary value problems for second-order elliptic equations 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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##### References:
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