A finite difference discretization method for elliptic problems on composite grids (Q1916051)

A simple finite difference discretization method for elliptic boundary value problems on composite grids is derived and studied. A theoretical basis for this study is the maximum principle and the analysis of the discretization error. The bounds for the error depend on the grid sizes of the coarse and fine grids, the interpolation used along the coarse/fine grids interface, and on the smoothness of the solution. In contrast with existing results, the error bounds derived in this paper do not depend on the quotient of the coarse and fine grid sizes. The developed technique is general and can be used in more general equations and approximations.