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.
Original language | English |
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Pages (from-to) | 2029-2049 |
Number of pages | 21 |
Journal | SIAM Journal on Scientific Computing |
Volume | 25 |
Issue number | 6 |
DOIs | |
Publication status | Published - 25 Jul 2006 |
Keywords
- saddle-point problems
- field-of-values-equivalence
- norm-equivalence
- mixed finite elements
- preconditioned Krylov methods