Multiscale asymptotic analysis and numerical simulation for second elliptic problems with oscillating coefficients in parallelotope periodic structure

In this paper we discuss the multiscale asymptotic expansion for a kind of general second order elliptic problem with rapidly oscillating coefficients in n-D parallelotope periodic structure. Based on the theoretical results, we investigate exhaustively the multiscale finite element algorithm. Numerical simulations are carried out to validate the proposed method of this paper.