Improved difference schemes for the Dirichlet problem of Poisson's equation in the neighbourhood of corners

Summary The standard 5-point difference scheme for the model problem u=f on a special polygonal domain with given boundary values is modified at a few points in the neighbourhood of the corners in such a way that the order of convergence at interior points is the same as in the case of a smooth boundary. As a side result improved error bounds for the usual method in the neighbourhood of corners are given.