A two-grid method for an elliptic equation with boundary layers on a Shishkin mesh

In this article, we consider a linear elliptic equation with regular and parabolic boundary layers. To solve this equation, we used an upwind difference scheme on a Shishkin mesh, possessing the property of the uniform convergence with respect to a small parameter. We investigated the problem of decreasing the required number of arithmetic operations for implementation of the difference scheme on the basis of a two-grid method, and studied the Richardson method aimed at improving the accuracy of this scheme. Here, we present results of some numerical experiments.