A Finite Volume Scheme for Solving Elliptic Boundary Value Problems on composite Grids

摘要

We present a finite volume scheme for solving elliptic boundary values problems with solutions that have one or a few small regions with high activity. The scheme results form combining the local defect correction method (LDC), introduced in [11], 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. For the LDC method in its standard from, the discrete conservation property, which is one of the main Attractive feature of a finite volume method, is lost for the composite grid approximation. For the Modified LDC method we present here, discrete conservation holds for the composite grid solution, Too.