A class of iterative methods for solving saddle point problems

Randolph E. Bank, Bruno D. Welfert, Harry Yserentant

Research output: Contribution to journalArticlepeer-review

176 Scopus citations


We consider the numerical solution of indefinite systems of linear equations arising in the calculation of saddle points. We are mainly concerned with sparse systems of this type resulting from certain discretizations of partial differential equations. We present an iterative method involving two levels of iteration, similar in some respects to the Uzawa algorithm. We relate the rates of convergence of the outer and inner iterations, proving that, under natural hypotheses, the outer iteration achieves the rate of convergence of the inner iteration. The technique is applied to finite element approximations of the Stokes equations.

Original languageEnglish (US)
Pages (from-to)645-666
Number of pages22
JournalNumerische Mathematik
Issue number7
StatePublished - Jul 1 1989
Externally publishedYes


  • Subject Classifications: AMS(MOS): 65F10, 65N20, 65N30, CR: G 1.8

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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