Deterministic homogenization for media with barriers
Vsevolod Laptev · Discrete and Continuous Dynamical Systems - S · 2014
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. In this article we consider coefficients with barriers. We show how the averaged coefficient may be inadequate near the barriers and proposea generalization which can detect the potential problems and improve the accuracy of the averaged solution.