Multigrid Methods for Variational Problems: Further Results

Abstract

In an earlier paper [SIAM J. Numer. Anal., 19 (1982), pp. 924–929], we developed a convergence theory for a class of multigrid methods applied to positive definite self-adjoint differential boundary value problems, where the multigrid process used W-cycling and Richardson’s iteration. In the present paper, we extend this theory to include V-cycling and more general relaxation schemes such as Jacobi and (arbitrarily ordered) Gauss-Seidel.