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

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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. 
@article{UZKU_2009_151_3_a5,
     author = {I. B. Badriev and I. N. Ismagilov and L. N. Ismagilov and G. I. Mukhamadullina},
     title = {Numerical solving of stationary anisotropic filtration problems},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {74--84},
     publisher = {mathdoc},
     volume = {151},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a5/}
}
TY  - JOUR
AU  - I. B. Badriev
AU  - I. N. Ismagilov
AU  - L. N. Ismagilov
AU  - G. I. Mukhamadullina
TI  - Numerical solving of stationary anisotropic filtration problems
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2009
SP  - 74
EP  - 84
VL  - 151
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a5/
LA  - ru
ID  - UZKU_2009_151_3_a5
ER  - 
%0 Journal Article
%A I. B. Badriev
%A I. N. Ismagilov
%A L. N. Ismagilov
%A G. I. Mukhamadullina
%T Numerical solving of stationary anisotropic filtration problems
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2009
%P 74-84
%V 151
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a5/
%G ru
%F UZKU_2009_151_3_a5
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/