Stopping criteria for mixed finite element problems

We study stopping criteria that are suitable in the solution by Krylov space based methods of linear and non linear systems of equations arising from the mixed and the mixed-hybrid finite-element approximation of saddle point problems. Our approach is based on the equivalence between the Babuska and...

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Bibliographic Details
Published inElectronic transactions on numerical analysis Vol. 29; p. 178
Main Authors Arioli, M, Loghin, D
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.12.2007
Subjects
Approximation theory
Equations
Finite element method
Methods
Properties
Topological spaces
United Kingdom
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ISSN1068-9613
1097-4067

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Summary:We study stopping criteria that are suitable in the solution by Krylov space based methods of linear and non linear systems of equations arising from the mixed and the mixed-hybrid finite-element approximation of saddle point problems. Our approach is based on the equivalence between the Babuska and Brezzi conditions of stability which allows us to apply some of the results obtained in Arioli, Loghin and Wathen [1]. Our proposed criterion involves evaluating the residual in a norm defined on the discrete dual of the space where we seek a solution. We illustrate our approach using standard iterative methods such as MINRES and GMRES. We test our criteria on Stokes and Navier-Stokes problems both in a linear and nonlinear context. Key words. augmented systems, mixed and mixed-hybrid finite-element, stopping criteria, Krylov subspaces method AMS subject classifications. 65F10, 65F35, 65F50, 65N30
ISSN:1068-9613
1097-4067