On the convergence of difference schemes for the approximation of solutionsu ? W 2 m (m>0.5) of elliptic equations with mixed derivatives

Abstract

The paper deals with such estimates of the rate of convergence of difference methods, which are compatible with the smoothness of the exact solutionu ? W 2 m (Ω),m>0.5, of elliptic equations with mixed derivatives: The error in the norm of the discrete Sobolev spaceW 2 s (?), ? denoting the set of grid points, is shown to be of the orderO(|h| m?s), 0?s<m.