Journal
NUMERISCHE MATHEMATIK
Volume 130, Issue 3, Pages 517-540Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00211-014-0674-5
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Funding
- Austrian Science Fund (FWF) [J3362-N25]
- Austrian Science Fund (FWF) [J 3362] Funding Source: researchfish
- Austrian Science Fund (FWF) [J3362] Funding Source: Austrian Science Fund (FWF)
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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.
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