Geodesic
Numerical solving of stationary anisotropic filtration problems
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 74-84
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The paper is devoted to the methods of numerical solving of stationary filtration problems of non-compressible fluid following the nonlinear multi-valued anisotropic filtration law with limiting gradient. This problem is mathematically formulated in the form of variational inequality of the second kind in Hilbert space with inversely strongly monotone operator. The functional occurring in this variational inequality is a sum of several lower semi-continuous convex proper functionals. For the solution of the considered variational inequality the splitting method is offered. This method allows finding both the pressure and the filtration velocity. The results of numerical experiments are presented.
Keywords: seepage theory, anisotropic filtration law, variational inequality, inversely strongly monotone operator, iterative process. 
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I. B. Badriev; I. N. Ismagilov; L. N. Ismagilov; G. I. Mukhamadullina. Numerical solving of stationary anisotropic filtration problems. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 74-84. http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a5/

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