A robust multigrid method for the time-dependent Stokes problem
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.
Cite
@article{arxiv.1502.04070,
title = {A robust multigrid method for the time-dependent Stokes problem},
author = {Stefan Takacs},
journal= {arXiv preprint arXiv:1502.04070},
year = {2016}
}
Comments
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)