A new approximate method for second order elliptic problems with rapidly oscillating coefficients based on the method of multiscale asymptotic expansions

In this paper, we consider second order elliptic problems with rapidly oscillating coefficients. On basis of [O.A. Oleinik, A.S. Shamaev, G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization, North-Holland, Amsterdam, 1992; Wen-ming He, Jun-zhi Cui, A pointwise estimate on the 1-order approximation of , IMA J. Appl. Math. 70 (2005) 241–269] we propose a new approximate method to solve these problems. Of course, we present its error estimate.