A class of iterative methods for solving saddle point problems

Randolph E. Bank, Bruno Welfert, Harry Yserentant

Research output: Contribution to journalArticle

155 Citations (Scopus)

Abstract

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
Volume56
Issue number7
DOIs
StatePublished - Jul 1989
Externally publishedYes

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Saddle Point Problems
Iterative methods
Linear equations
Partial differential equations
Iteration
Rate of Convergence
Uzawa Algorithm
Indefinite Systems
Stokes Equations
Saddlepoint
System of Linear Equations
Finite Element Approximation
Partial differential equation
Discretization
Class
Numerical Solution

Keywords

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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Mathematics(all)

Cite this

A class of iterative methods for solving saddle point problems. / Bank, Randolph E.; Welfert, Bruno; Yserentant, Harry.

In: Numerische Mathematik, Vol. 56, No. 7, 07.1989, p. 645-666.

Research output: Contribution to journalArticle

Bank, Randolph E. ; Welfert, Bruno ; Yserentant, Harry. / A class of iterative methods for solving saddle point problems. In: Numerische Mathematik. 1989 ; Vol. 56, No. 7. pp. 645-666.
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