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Numerical boundary corrector for elliptic equations with rapidly oscillating periodic coefficients

We develop a numerical method to solve 
 
 
(1) 
 
 
 
where the matrix a(y)=(aij(y)) is symmetric positive definite, whose entries are periodic functions of y with periodic cell Y. More specifically we assume . It is also assumed that there exists positive constants γa and βa such that for all and . The major goal in this paper is to develop a numerical approximation scheme on a mesh size h > e (or h≫e) with quasi-optimal approximation on L2 and broken H1 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 flow through porous media and composite materials. Copyright © 2005 John Wiley & Sons, Ltd.