Analysis of Preconditioners for Saddle-Point Problems

Authors:
D. Loghin;A. J. Wathen
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2004

Citing 0
Cited 6

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Abstract

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.