CONVERGENCE OF A MULTIGRID METHOD FOR ELLIPTIC-EQUATIONS WITH HIGHLY OSCILLATORY COEFFICIENTS

Standard multigrid methods are not so effective for equations with hig hly oscillatory coefficients. New coarse grid operators based on homog enized operators are introduced to restore the fast convergence rate o f multigrid methods. Finite difference approximations are used for the discretization of the equations. Convergence analysis is based on the homogenization theory. Proofs are given for a two-level multigrid met hod with the homogenized coarse grid operator for two classes of two-d imensional elliptic equations with Dirichlet boundary conditions.