Analysis of preconditioners for saddle-point problems

Journal article

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 Babuška-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.

Authors: Loghin, D; Wathen, A

• Publication status: Published
• Journal: SIAM JOURNAL ON SCIENTIFIC COMPUTING
• Volume: 25
• Issue: 6
• Pages: 2029-2049
• Publication date: 2004-01-01
• DOI: 10.1137/S1064827502418203
• EISSN: 1095-7197
• ISSN: 1064-8275
• Language: English
• Keywords: preconditioned Krylov methods; field-of-values-equivalence; mixed finite elements; saddle-point problems; norm-equivalence