On the Analysis of Block Smoothers for Saddle Point Problems

Abstract

We discuss several Uzawa-type iterations as smoothers in the context of multigrid schemes for saddle point problems. A unified framework to analyze the smoothing properties is presented. The introduction of a new symmetric variant allows us to obtain estimates for popular lower and upper block triangular variants. Numerical experiments for a low order stable and a stabilized P1-conforming discretization for the Stokes problem illustrate the theory. Finally, large-scale three-dimensional examples demonstrate the potential of this class of smoothers.