Multigrid methods for symmetric variational problems: a general theory and convergence estimates for usual smoothers

摘要

This work is concerned with studying a class of multigrid methods constructed on a sequence of nested subspaces of the Hilbert space on which the variational problem to solve is defined. It gives a general convergence result through bounds on the convergence rate in the “energy norm” for any multigrid scheme (including the V-cycle). The bounds are made precise for some usual smoothers. In the case of a simple model problem, the computed bounds show the fitness of the various factors considered.