An iterative finite volume discretization method for solving elliptic boundary value problems on locally refined grids

We present a finite volume scheme for solving elliptic boundary value problems with solutions that have one or a few small regions with high activity. The scheme results from combining the local defect correction method (LDC), introduced in [4], with standard finite volume discretizations on a global coarse and on local fine uniform grids. The iterative discretization method that is obtained in this way yields a discrete approximation of the continuous solution on a composite grid. It is shown, that the composite grid solution satisfies a discrete conservation property.