Geodesic
Stopping criteria for mixed finite element problems
Electronic transactions on numerical analysis, Tome 29 (2008).

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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 Babu$\check $ska 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.
Classification : 65F10, 65F35, 65F50, 65N30
Keywords: augmented systems, mixed and mixed-hybrid finite-element, stopping criteria, Krylov subspaces method 
@article{ETNA_2008__29__a2,
     author = {Arioli, M. and Loghin, D.},
     title = {Stopping criteria for mixed finite element problems},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {29},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__29__a2/}
}
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JO  - Electronic transactions on numerical analysis
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%A Arioli, M.
%A Loghin, D.
%T Stopping criteria for mixed finite element problems
%J Electronic transactions on numerical analysis
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%F ETNA_2008__29__a2
Arioli, M.; Loghin, D. Stopping criteria for mixed finite element problems. Electronic transactions on numerical analysis, Tome 29 (2008). http://geodesic.mathdoc.fr/item/ETNA_2008__29__a2/