Crosswind smear and pointwise errors in streamline diffusion finite element methods

Source 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 {h^{5/4}} under local smoothness assumptions.