Multigrid methods for symmetric variational problems: A general theory and convergence estimates for usual smoothers (Q1098240)

The authors consider multigrid methods for symmetric variational problems on a sequence of nested subspaces of a Hilbert space. A general convergence result through bounds on the convergence rate in the energy norm is derived. The bounds are made precise for some usual smoothers. As an illustration a one-dimensional Poisson equation is given. It is an interesting paper and the reviewer believes that similar results can be obtained for variational inequalities of elliptic type.