An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem
An upwind difference scheme on a novel layer-adapted mesh (a modification of Shishkin piecewise uniform mesh) is considered for a linear singularly perturbed convection-diffusion problem in two dimensions. It is proved that the upwind scheme on the modified Shishkin mesh is first-order convergent in the discrete \(L^\infty\) norm. The new mesh yields more accurate results than simple upwinding on a standard Shishkin mesh, even though it requires essentially the same computational effort. Numerical experiments are presented, which confirm the theoretical results.
scientific article; zbMATH DE number 1367869