  In this article, we discuss several classes of Uzawa smoothers for the
application in multigrid methods in the context of saddle point problems.
Beside commonly used variants, such as the inexact and block factorization
version, we also introduce a new symmetric method, belonging to the class of
Uzawa smoothers. For these variants we unify the analysis of the smoothing
properties, which is an important part in the multigrid convergence theory.
These methods are applied to the Stokes problem for which all smoothers are
implemented as pointwise relaxation methods. Several numerical examples
illustrate the theoretical results.
