Crosswind Smear and Pointwise Errors in Streamline Diffusion Finite Element Methods

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 under local smoothness assumptions.