A robust all-at-once multigrid method for the Stokes control problem
Abstract
In this paper we present an all-at-once multigrid method for a distributed Stokes control problem (velocity tracking problem). For solving such a problem, we use the fact that the solution is characterized by the optimality system (Karush-Kuhn-Tucker-system). The discretized optimality system is a large-scale linear system whose condition number depends on the grid size and on the choice of the regularization parameter forming a part of the problem. Recently, block-diagonal preconditioners have been proposed, which allow to solve the problem using a Krylov space method with convergence rates that are robust in both, the grid size and the regularization parameter or cost parameter. In the present paper, we develop an all-at-once multigrid method for a Stokes control problem and show robust convergence, more precisely, we show that the method converges with rates which are bounded away from one by a constant which is independent of the grid size and the choice of the regularization or cost parameter.
Keywords
Cite
@article{arxiv.1502.04121,
title = {A robust all-at-once multigrid method for the Stokes control problem},
author = {Stefan Takacs},
journal= {arXiv preprint arXiv:1502.04121},
year = {2015}
}
Comments
The research was funded by the Austrian Science Fund (FWF): J3362-N25. The original publication is available at www.springerlink.com. in Numerische Mathematik. 2014. arXiv admin note: substantial text overlap with arXiv:1502.04070