Finite Difference Discretization Method for Elliptic Problems on Composite Grids

摘要

In this paper, we discuss a simple finite difference method for thediscretization of elliptic boundary value problems on composite grids. For the model problem of the Poisson equation, we prove stability of the discrete operator and bounds for the global discretization error. These bounds clearly show how the discretization error depends on the grid size of the coarse grid, on the grid size of the local fine grid and on the order of the interpolation used on the interface. Furthermore, the constants in these bounds do not depend on the quotient of coarse grid size and fine grid size. We also discuss an efficient solution method for the resulting composite grid algebraic problem.