Analysis of preconditioners for saddle-point problems

Daniel Loghin, AJ Wathen

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)


Mixed finite element formulations give rise to large, sparse, block linear systems of equations, the solution of which is often sought via a preconditioned iterative technique. In this work we present a general analysis of block-preconditioners based on the stability conditions inherited from the formulation of the finite element method (the Babuska--Brezzi, or inf-sup, conditions). The analysis is motivated by the notions of norm-equivalence and field-of-values-equivalence of matrices. In particular, we give sufficient conditions for diagonal and triangular block-preconditioners to be norm- and field-of-values-equivalent to the system matrix.
Original languageEnglish
Pages (from-to)2029-2049
Number of pages21
JournalSIAM Journal on Scientific Computing
Issue number6
Publication statusPublished - 25 Jul 2006


  • saddle-point problems
  • field-of-values-equivalence
  • norm-equivalence
  • mixed finite elements
  • preconditioned Krylov methods


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