We consider the multigrid solution of the generalized Stokes equations with a segre- gated (i.e., equationwise) Gauss–Seidel smoother based on a Uzawa-type iteration. We analyze the smoother in the framework of local Fourier analysis, and obtain an analytic bound on the smoothing factor showing uniform performance for a family of Stokes problems. These results are confirmed by the numerical computation of the two-grid convergence factor for different types of grids and dis- cretizations. Numerical results also show that the actual convergence of the W-cycle is approximately the same as that obtained by a Vanka smoother, despite this latter smoother being significantly more costly per iteration step.
SIAM Journal on Scientific Computing
Scientific Computing

Gaspar, F., Notay, Y., Oosterlee, K., & Rodrigo, C. (2014). A simple and efficient segregated smoother for the discrete Stokes equations. SIAM Journal on Scientific Computing, 36(3), A1187–A1206. doi:10.1137/130920630