ON A NOVEL MESH FOR THE REGULAR BOUNDARY-LAYERS ARISING IN ADVECTION-DOMINATED TRANSPORT IN 2 DIMENSIONS

Upwind finite difference operators on uniform meshes are well known to be unsuitable for the numerical solution of singularly perturbed part ial differential equations, in the sense that, in the neighbourhood of the boundary layers, the error in the numerical approximation may inc rease as the mesh is refilled. Recently, on the other hand, it has bee n predicted theoretically that the use of upwind finite difference ope rators on specially designed piecewise uniform meshes guarantees the d ecrease of the nodal error to zero as the number of mesh elements incr eases. In the paper the general theorem is quoted and its prediction i s validated by numerical experiment for a specific linear advection-do minated transport equation in two dimensions. Experimental values of t he convergence rate are obtained, which also agree with the theoretica l estimates.