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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.

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
Full Text: DOI
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