Application of the two-grid medhod for solving a singularly perturbed elliptic problem

Аннотация

A two-grid method for the numerical solution of a singularly perturbed elliptic prob lem using the Bakhvalov mesh is studied. A scheme of upwind differences is used, which has the property of convergence on this grid, which is uniform in a small parameter. The Seidel iterative method is used to find the difference scheme solution. Previously, the use of the Bakhvalov mesh in the two-grid method has not been studied. It is numerically shown that the use of the two-grid method leads to a reduction in computational costs. In addition, it is shown that based on the Richardson extrapolation method, it is possible to improve the accuracy of the difference scheme.