Elliptic equations with rough coefficients: analytical and finite difference approaches

Vladimir Druskin
Schlumberger Doll Research

Abstract: We consider the problem of calculating a potential function in a two dimensional inhomogeneous medium which varies locally in only one direction. We propose a staggered finite difference scheme on a regular Cartesian grid with a special cell homogenizanion. This homogenizanion allows for the change in conductivity to be in any direction with respect to the grid and does not require the grid to be small compared to the layering. We give a convergence result and numerical experiments which suggest that the new homogenizanion works much better than the standard homogenization.