Numerische Mathematik

, Volume 90, Issue 4, pp 665–688

Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations

  • Howard C. Elman
  • David J. Silvester
  • Andrew J. Wathen
Original article

DOI: 10.1007/s002110100300

Cite this article as:
Elman, H., Silvester, D. & Wathen, A. Numer. Math. (2002) 90: 665. doi:10.1007/s002110100300


We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier-Stokes equations. With a combination of analytic and empirical results, we study the effects of fundamental parameters on convergence. We demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. The structure of these distributions is independent of the discretization mesh size, but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller. These characteristics are directly correlated with the convergence properties of iterative solvers.

Mathematics Subject Classification (1991): 65N22

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Howard C. Elman
    • 1
  • David J. Silvester
    • 2
  • Andrew J. Wathen
    • 3
  1. 1.Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA; e-mail: US
  2. 2.Department of Mathematics, University of Manchester, Institute of Science and Technology, Manchester M601QD, UK; e-mail: GB
  3. 3.Oxford University, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX13QD, UK; e-mail: GB