Convergence of a Multigrid Method for Elliptic Equations with Highly Oscillatory Coefficients
Bjorn E. Engquist, Erding Luo · SIAM Journal on Numerical Analysis · 1997
Standard multigrid methods are not so effective for equationswith highly oscillatory coefficients. New coarse grid operators based on homogenized operators are introduced to restore the fast convergence rate of 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 method with the homogenized coarse grid operator for two classes of two-dimensional elliptic equations with Dirichlet boundary conditions.