On numerical averaging of the conductivity coefficient using two-scale extensions

In this article we compare solutions to elliptic problems having rapidly oscillated conductivity (permeability, etc) coefficient with solutions to corresponding homogenized problems obtained from two-scale extensions of the initial coefficient. The comparison is done numerically on several one and two dimensional test problems with randomly generated coefficients for different intensities of oscillation. The dependency of the approximation error on the size of averaging is investigated.