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A convergence of an implicit difference scheme for the saturated-unsaturated filtration consolidation problem

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Abstract

An implicit difference scheme for the problem of saturated-unsaturated filtration consolidation is considered and analyzed under the condition when a part of the boundary is semi-permeable. The penalty method is applied to establish the existence of a solution to the difference problem. The convergence of the difference scheme is studied under minimal assumptions on the smoothness of the original data: the convergence of the piecewise-constant extensions of the difference solution to the generalized solution of the problem is proved.

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Authors and Affiliations

  1. Kazan Federal University, Kremlevskaya ul. 18, Kazan, 420008, Tatarstan, Russia

    M. F. Pavlova & E. V. Rung

Authors
  1. M. F. Pavlova
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  2. E. V. Rung
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Correspondence to M. F. Pavlova.

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Original Russian Text © M.F. Pavlova, E.V. Rung, 2012, published in Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2012, Vol. 154, No. 4, pp. 33–48.

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Pavlova, M.F., Rung, E.V. A convergence of an implicit difference scheme for the saturated-unsaturated filtration consolidation problem. Lobachevskii J Math 34, 392–405 (2013). https://doi.org/10.1134/S1995080213040057

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  • DOI: https://doi.org/10.1134/S1995080213040057

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