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

Abstract

A linear elliptic equation with regular and parabolic boundary layers is considered. It is solved by using an upwind difference scheme on a Shishkin mesh with the property of uniform convergence with respect to a small parameter. The problem of reducing the number of arithmetic operations required to implement the difference scheme on the basis of a two-grid method is investigated. The application of the Richardson extrapolation method to increase the accuracy of the difference scheme is studied. Results of numerical experiments are presented.