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Persistent URL http://purl.org/net/epubs/work/40516
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Record Id 40516
Title Dual variable methods for mixed-hybrid finite element approximation of the potential fluid flow problem in porous media
Contributors
Abstract Mixed-hybrid finite element discretization of the Darcy's law and the continuity equation that describe the potential fluid flow problem in porous media leads to symmetric indefinite linear systems with a particular block structure. In this paper we consider an approach for a solution of a projected system. A fundamental cycle null-space basis of the whole off-diagonal block in the system matrix and on subsequent iterative solution of a projected system. 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 basis may be theoretically rather ill-conditioned while the orthogonal null-space basis of its certain sub-block 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 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.
Organisation CCLRC , CSE , CSE-NAG
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Funding Information
Related Research Object(s): 40514
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Language English (EN)
Type Details URI(s) Local file(s) Year
Journal Article Special volume on saddle-point problems: numerical solution & applications. 2006