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 Gε x0 , 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. © 2007 Elsevier Inc. All rights reserved