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Crosswind smear and pointwise errors in streamline diffusion finite element methods

Authors: C. Johnson, A. H. Schatz and L. B. Wahlbin
Journal: Math. Comp. 49 (1987), 25-38
MSC: Primary 65N30; Secondary 35B25
MathSciNet review: 890252
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Abstract: For a model convection-dominated singularly perturbed convection-diffusion problem, it is shown that crosswind smear in the numerical streamline diffusion finite element method is minimized by introducing a judicious amount of artificial crosswind diffusion. The ensuing method with piecewise linear elements converges with a pointwise accuracy of almost $ {h^{5/4}}$ under local smoothness assumptions.

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Keywords: Finite element method, convection dominated
Article copyright: © Copyright 1987 American Mathematical Society