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Numerische Mathematik

, Volume 105, Issue 1, pp 159–191 | Cite as

Uniform preconditioners for a parameter dependent saddle point problem with application to generalized Stokes interface equations

  • Maxim A. Olshanskii
  • Jörg Peters
  • Arnold Reusken
Article

Abstract

We consider an abstract parameter dependent saddle-point problem and present a general framework for analyzing robust Schur complement preconditioners. The abstract analysis is applied to a generalized Stokes problem, which yields robustness of the Cahouet-Chabard preconditioner. Motivated by models for two-phase incompressible flows we consider a generalized Stokes interface problem. Application of the general theory results in a new Schur complement preconditioner for this class of problems. The robustness of this preconditioner with respect to several parameters is treated. Results of numerical experiments are given that illustrate robustness properties of the preconditioner.

Keywords

Generalized Stokes equations Interface problem Two-phase flow Preconditioning Schur complement 

AMS Subject Classifications

65N15 65N22 65N30 65F10 

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Maxim A. Olshanskii
    • 1
  • Jörg Peters
    • 2
  • Arnold Reusken
    • 2
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Institut für Geometrie und Praktische MathematikRWTH-AachenAachenGermany

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