Analysis of a local defect correction approach on composite grids

In this paper we consider the problem of discretization on a composite grid that consists of a global uniform coarse grid and a local uniform fine grid. For elliptic problems a local defect correction approach is described. The error of the resulting approximation is analysed. It follows that in general the accuracy ofthis approximation is (much) better than the accuracy of an approximation that results from an approach without local defect correction. The use of a "buffer zone " in the local defect correction approach appears to be essential for several problems. We discuss when such a "buffer zone " is necessary to obtain satisfactory results. A.M.S. Classifications