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Preconditioners for the pressure-correction method applied to the unsteady stokes problem

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Abstract

In this paper, the unsteady Stokes problem is considered and also the pressure-correction method for the problem is described. At a fixed time level, we reduce the problem to two summetric positive definite problems which depend on a time step parameter. Linear systems that arise from the problems are large, sparse, symmetric, positive definite and ill-conditioned as the time step tends to zero. Preconditioned problems based on an additive Schwarz method for solving the symmetric positive definite problems are derived and preconditioners are defined implicitly. It will be shown that the rate of convergence is independent of the mesh parameters as well as the time step size

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Author information

Correspondence to N. Ghahreman.

Additional information

Navid Ghahreman received his B. Sc and M. Sc from Ferdowsi University of Mashhad, Iran and he received Ph.D under the direction of Dr. Asghar Kerayechian from Ferdowsi University of Mashhad. Since 2002 he has been working at the Ferdowsi University of Mashhad. His research interests are mainly numerical analysis and computational methods for fluid dynamics

Asghar Kerayechian received his B. Sc from University of Tehran, Iran, his M. Sc from University of Southampton, England and Ph.D at Colorado state University, USA under the supervision of prof. David Zachmann. Since 1981 he has been working at the Ferdowsi University of Mashhad. He spent a sabbatical year at the Australian National University. His research interests are partial differential equations and numerical analysis.

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Ghahreman, N., Kerayechian, A. Preconditioners for the pressure-correction method applied to the unsteady stokes problem. JAMC 16, 307–321 (2004). https://doi.org/10.1007/BF02936171

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AMS Mathematics Subject Classification

  • 65M55
  • 76D07
  • 65N30
  • 65F10

Key words and phrases

  • Overlapping domain decomposition preconditioners
  • unsteady Stokes problem
  • pressure-correction method