Deterministic homogenization for media with barriers

Abstract

Averaging coefficient in a second order elliptic equation is a well known and important model problem. Additional to non-periodic rapid oscillations, the coefficient may contain barriers and channels - long and narrow bodies with low or high values of the coefficient. When the length of such structures is comparable with the problem size - there is no scale separation. &nbsp In this article we consider coefficients with barriers. We show how the averaged coefficient may be inadequate near the barriers and propose a generalization which can detect the potential problems and improve the accuracy of the averaged solution.