Numerical boundary corrector for elliptic equations with rapidly oscillating periodic coefficients

where the matrix a(y)= (aij(y)) is symmetric positive de nite, whose entries are periodic functions of y with periodic cell Y . More speci cally we assume aij ∈C1; ( ); ¿ 0. It is also assumed that there exists positive constants a and a such that a‖ ‖2 6 aij(y) i j 6 a‖ ‖2 for all ∈ 2 and y∈ Y . The major goal in this paper is to develop a numerical approximation scheme on a mesh size h¿ (or h ) with quasi-optimal approximation on L and broken H 1 norms. The new method is based on asymptotic analysis and a careful treatment of the boundary corrector term. This kind of equation has applications in areas such as the study of ow through porous media and composite materials. Copyright ? 2005 John Wiley & Sons, Ltd.