Literature cited
A. D. Lyashko and M. M. Karchevskii, “Investigation of nonlinear problems of seepage theory,” in: Proc. of Seminar on Boundary-Value Problems [in Russian], No. 11, Izd. Kazan' Univ. (1974), pp. 64–72.
A. D. Lyashko and M. M. Karchevskii, “On solving some nonlinear problems of seepage theory,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 6, 73–81 (1975).
A. D. Lyashko, I. B. Badriev, and M. M. Karchevskii, “On variational method for equations with discontinuous monotone operators,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 11, 63–69 (1978).
M. M. Karchevskii and I. B. Badriev, “Nonlinear problems of seepage theory,” in: Numerical Methods of Mechanics of Continuous Media [in Russian], Vol. 10, Novosibirsk (1979), pp. 63–78.
A. V. Lapin, “Investigation of some problems of nonlinear seepage theory,” Zh. Vychisl. Mat. Mat. Fiz.,19, No. 3, 689–700 (1979).
A. V. Lapin and M. M. Karchevskii, “Investigation of a difference scheme for a nonlinear stationary problem of seepage theory,” Issled. Prikl. Mat., Kazan' Univ., No. 6, 26–31 (1979).
I. B. Badriev and M. M. Karchevskii, “Application of the duality method to solving nonlinear problems of seepage theory with a limiting gradient,” Differen. Uravn.,18, No. 7, 1133–1144 (1982).
I. B. Badriev, “Difference schemes for nonlinear problems of seepage theory with a discontinuous law,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 3–12 (1983).
A. D. Lyashko and M. M. Karchevskii, “Difference methods for nonlinear problems of seepage theory,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 28–45 (1983).
I. B. Badriev, “On regularization of the nonlinear problem of seepage theory with a limiting gradient,” Issled. Prikl. Mat., Kazan' Univ., No. 10, 162–175 (1984).
I. B. Badriev, “On convergence of an Uzawa-type iterative method for solving the stationary problem of seepage theory with a limiting gradient,” Issled. Prikl. Mat., Kazan' Univ., No. 13, 56–75 (1985).
I. Ekeland and R. Temam, Convex Analysis and Variational Problems [Russian translation], Mir, Moscow (1979).
R. Temam, Navier-Stokes Equations [Russian translation], Mir, Moscow (1981).
S. G. Mikhlin, Numerical Implementation of Variational Methods [in Russian], Nauka, Moscow (1966).
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Translated from Issledovaniya po Prikladnoi Matematike, No. 16, pp. 17–34, 1989.
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Badriev, I.B., Pankratova, O.V. Mixed finite-element method for nonlinear stationary problems of seepage theory. J Math Sci 61, 2405–2416 (1992). https://doi.org/10.1007/BF01100574
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DOI: https://doi.org/10.1007/BF01100574