Iterative solution techniques for the stokes and Navier‐Stokes equations

Alison Ramage, Andrew J. Wathen

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


The linear system arising from a Lagrange‐Galerkin mixed finite element approximation of the Navier–Stokes and continuity equations is symmetric indefinite and has the same block structure as a system arising from a mixed finite element discretization of a Stokes problem. This paper considers the iterative solution of such a system, comparing the performance of the one‐level preconditioned conjugate residual method for indefinite matrices with that of a more traditional two‐level pressure correction approach. Asymptotic estimates for the amount of work involved in each method are given together with the results of related numerical experiments.

Original languageEnglish
Pages (from-to)67-83
Number of pages17
JournalInternational Journal for Numerical Methods in Fluids
Issue number1
Publication statusPublished - 1 Jan 1994


  • conjugate gradients
  • mixed finite elements
  • Navier–Stokes
  • numerical experiments


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