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

Johnson, C.; Schatz, A. H.; Wahlbin, L. B.

Math. Comput. 49, 25-38 (1987).

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

MSC:

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

Keywords:

streamline diffusion finite element method; convection dominated; singularly perturbed convection-diffusion equation; upstream finite element method; crosswind artificial diffusion