A robust multigrid method for the time-dependent Stokes problem
arXiv:1502.04070 · doi:10.1137/140969658
Abstract
In the present paper we propose a coupled multigrid method for generalized Stokes flow problems. Such problems occur as subproblems in implicit time-stepping approaches for time-dependent Stokes problems. The discretized Stokes system is a large-scale linear system whose condition number depends on the grid size of the spatial discretization and of the length of the time step. Recently, for this problem a coupled multigrid method has been proposed, where in each smoothing step a Poisson problem has to be solved (approximately) for the pressure field. In the present paper, we propose a coupled multigrid method where the solution of such sub-problems is not needed. We prove that the proposed method shows robust convergence behavior in the grid size of the spatial discretization and of the length of the time-step.
The research was funded by the Austrian Science Fund (FWF): J3362-N25. (The final version is available at http://epubs.siam.org/doi/10.1137/140969658)