Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media

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dc.contributor.authorArioli, M.
dc.contributor.authorMaryška, Jiří
dc.contributor.authorRozložník, Miroslav
dc.contributor.authorTůma, Miroslav
dc.date.accessioned2016-05-24
dc.date.available2016-05-24
dc.date.issued2006
dc.description.abstractMixed-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. Alternatively, the orthogonal null-space basis of the sub-block used to enforce continuity over faces can be easily constructed. In the former case, the resulting projected system is symmetric positive definite and so the conjugate gradient method can be applied. The projected system in the latter case remains indefinite and the preconditioned minimal residual method (or the smoothed conjugate gradient method) should be used. The theoretical rate of convergence for both algorithms is discussed and their efficiency is compared in numerical experiments. Copyright © 2006, Kent State University.en
dc.formattext
dc.identifier.issn1068-9613
dc.identifier.scopus2-s2.0-33646365072
dc.identifier.urihttps://dspace.tul.cz/handle/15240/16365
dc.identifier.urihttps://www.researchgate.net/publication/266841116_Dual_variable_methods_for_mixed-hybrid_finite_element_approximation_of_the_potential_fluid_flow_problem_in_porous_media
dc.language.isoen
dc.publisherTechnická Univerzita v Libercics
dc.publisherTechnical university of Liberec, Czech Republicen
dc.relation.ispartofElectronic Transactions on Numerical Analysisen
dc.sourcej-scopus
dc.sourcej-wok
dc.subjectFinite element methoden
dc.subjectPreconditioned iterative methodsen
dc.subjectSaddle-point problemen
dc.subjectSparse matricesen
dc.titleDual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous mediaen
dc.typeArticle
local.accessοpen
local.citation.epage40
local.citation.spage17
local.departmentInstitute of Information Technology and Electronics
local.facultyFaculty of Mechatronics, Informatics and Interdisciplinary Studies
local.fulltextyes
local.identifier.stagRIV/67985807:_____/06:00039327
local.identifier.wok237147300003
local.relation.volume22
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