Geodesic
Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media
Electronic transactions on numerical analysis, Tome 22 (2006), pp. 17-40
Mixed-hybrid finite element discretization of Darcy's law and the continuity equation that describe the potential fluid flow problem in porous media leads to symmetric indefinite saddle-point problems. In this paper we consider solution techniques based on the computation of a null-space basis of the whole or of a part of the left lower off-diagonal block in the system matrix and on the subsequent iterative solution of a projected system. This approach is mainly motivated by the need to solve a sequence of such systems with the same mesh but different material properties. A fundamental cycle null-space basis of the whole off-diagonal block is constructed using the spanning tree of an associated graph. It is shown that such a basis may be theoretically rather ill-conditioned.
Classification : 65F05, 65F50
Keywords: saddle-point problem, preconditioned iterative methods, sparse matrices, finite element method 
@article{ETNA_2006__22__a7,
     author = {Arioli,  M. and Mary\v{s}ka,  J. and Rozlo\v{z}n{\'\i}k,  M. and T\r{u}ma,  M.},
     title = {Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media},
     journal = {Electronic transactions on numerical analysis},
     pages = {17--40},
     year = {2006},
     volume = {22},
     zbl = {1112.65024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__22__a7/}
}
TY  - JOUR
AU  - Arioli,  M.
AU  - Maryška,  J.
AU  - Rozložník,  M.
AU  - Tůma,  M.
TI  - Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media
JO  - Electronic transactions on numerical analysis
PY  - 2006
SP  - 17
EP  - 40
VL  - 22
UR  - http://geodesic.mathdoc.fr/item/ETNA_2006__22__a7/
LA  - en
ID  - ETNA_2006__22__a7
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%A Arioli,  M.
%A Maryška,  J.
%A Rozložník,  M.
%A Tůma,  M.
%T Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media
%J Electronic transactions on numerical analysis
%D 2006
%P 17-40
%V 22
%U http://geodesic.mathdoc.fr/item/ETNA_2006__22__a7/
%G en
%F ETNA_2006__22__a7
Arioli,  M.; Maryška,  J.; Rozložník,  M.; Tůma,  M. Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media. Electronic transactions on numerical analysis, Tome 22 (2006), pp. 17-40. http://geodesic.mathdoc.fr/item/ETNA_2006__22__a7/