  The solution of saddle-point problems, such as the Stokes equations, is a
challenging task, especially in large-scale problems. Multigrid methods are one
of the most efficient solvers for such systems of equations and can achieve
convergence rates independent of the problem size. The smoother is a crucial
component of multigrid methods and significantly affects its overall
efficiency. We propose a Vanka-type smoother that we refer to as Restricted
Additive Vanka and investigate its convergence in the context of adaptive
geometric multigrid methods for the Stokes equations. The proposed smoother has
the advantage of being an additive method and provides favorable properties in
terms of algorithmic complexity, scalability and applicability to
high-performance computing. We compare the performance of the smoother with two
variants of the classical Vanka smoother using numerical benchmarks for the
Stokes problem. We find that the restricted additive smoother achieves
comparable convergence rates to the classical multiplicative Vanka smoother
while being computationally less expensive per iteration, which results in
faster solution runtimes.
