Geodesic
A study of an implicit difference scheme for the problem of saturated-unsaturated filtration consolidation
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 33-48

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An implicit difference scheme for the problem of saturated-unsaturated filtration consolidation under condition of semi-permeability on part of the boundary is constructed and investigated. Using the penalty method the existence of the solution to the difference problem is established. A study of the implicit convergence of the difference scheme is carried out under minimal propositions on the smoothness of the original conditions: the convergence of the piecewise-constant filling of the difference solution to the generalized solution of the problem under consideration is proved.
Mots-clés : filtration consolidation
Keywords: difference schemes, penalty method, convergence of difference scheme. 
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     author = {M. F. Pavlova and E. V. Rung},
     title = {A study of an implicit difference scheme for the problem of saturated-unsaturated filtration consolidation},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {33--48},
     publisher = {mathdoc},
     volume = {154},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a3/}
}
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M. F. Pavlova; E. V. Rung. A study of an implicit difference scheme for the problem of saturated-unsaturated filtration consolidation. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 33-48. http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a3/