Homogenization and multigrid

For elliptic partial differential equations with periodically oscillating c oefficients which may have large jumps. we prove robust convergence of a tw o-grid algorithm using a prolongation motivated by the theory of homogeniza tion. The corresponding Galerkin operator on the coarse grid turns out to b e a discretization of a diffusion operator with homogenized coefficients ob tained by solving discrete cell problems. This two-grid method is then embe dded inside a multi-grid cycle extending over both the fine and the coarse scale.