Crosswind smear and pointwise errors in streamline diffusion finite element methods. (English) Zbl 0629.65111

A singularly perturbed convection-diffusion equation \(u_ x+u=f+\delta u_{xx}+\epsilon u_{yy}\) is solved by an upstream finite element method. It is shown that when internal layers are present, the accuracy of the algorithm may be improved by a proper modification of the parameter \(\epsilon\), that is, by the addition of a crosswind artificial diffusion.
Reviewer: G.Hedstrom


65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35B25 Singular perturbations in context of PDEs
76R05 Forced convection
35K20 Initial-boundary value problems for second-order parabolic equations
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