Uniform preconditioners for the time dependent Stokes problem

Authors:
Kent-Andre Mardal;Ragnar Winther
Affiliations:
Simula Research Laboratory, University of Oslo, Department of Scientific Computing and Department of Informatics, 134, 1325, Lysaker, Norway;University of Oslo, Centre of Mathematics for Applications and Department of Informatics, 134, 1053 Blindern, 0316, Oslo, Norway
Venue:
Numerische Mathematik
Year:
2004

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Abstract

Implicit time stepping procedures for the time dependent Stokes problem lead to stationary singular perturbation problems at each time step. These singular perturbation problems are systems of saddle point type, which formally approach a mixed formulation of the Poisson equation as the time step tends to zero. Preconditioners for discrete analogous of these systems are discussed. The preconditioners uses standard positive definite elliptic preconditioners as building blocks and lead to condition numbers which are bounded uniformly with respect to the time step and the spatial discretization. The construction of the discrete preconditioners is related to the mapping properties of the corresponding continuous system.