Analysis of Preconditioners for Saddle-Point Problems
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.
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SIAM Journal on Scientific Computing
Pages: 2029 - 2049
ISSN (online): 1095-7197
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Copyright © 2004 Society for Industrial and Applied Mathematics.
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Published online: 25 July 2006
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