Skip to main content
Log in

Application of mixed schemes of the finite element method to the solution of problems of nonlinear filtration theory

  • Published:
Russian Mathematics Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. M. Farhloul, “A Mixed Finite Element Method for a Nonlinear Dirichlet Problem,” IMA. J. Num. Analysis 18, 121–132 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  2. M. Farhloul and H. Manouzi, “On a Mixed Finite Element Method for the p-Laplacian,” Canadian Applied Mathematics Quathrly 8(1), 67–78 (2000).

    MATH  MathSciNet  Google Scholar 

  3. M. M. Karchevskii and A. E. Fedotov, “One Version of the Mixed Finite Element Method for Quasilinear Elliptic Equations,” Issled. po Prikladnoi Matem., Kazansk. Gos., Univ., No. 24, 74–80 (2003).

  4. M. M. Karchevsky and A. E. Fedotov, “Error Estimates and Iterative Procedure for Mixed Finite Element Solution of Second-Order Quasi-Linear Elliptic Problems,” Computat. Methods in Appl. Math. 4(4), 445–463 (2004).

    MATH  MathSciNet  Google Scholar 

  5. M. M. Karchevskii, “One Approach to the Construction of Mixed FEM Schemes for Quasilinear Elliptic Equations,” in Proceedings of 5th All-Russian Seminar “Mesh Methods for Boundary-Value Problems and Their Applications,” Kazan, Russia, 2004 (Kazansk. Gos. Univ., Kazan, 2004), pp. 108–111.

    Google Scholar 

  6. M. M. Karchevskii and A. E. Fedotov, “A Mixed Finite Element Method for Quasilinear Degenerate Elliptic Equations,” Uchen. Zap. Kazansk. Univ. 147(3), 127–140 (2005).

    Google Scholar 

  7. M. M. Karchevskii and A. D. Lyashko, “On the Solution of Some Nonlinear Problems of Seepage Theory,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 6, 73–81 (1975) [Soviet Mathematics (Iz. VUZ) 19, No. 8 (1975)].

  8. O. A. Zadvornov, “Investigation of a Nonlinear Stationary Filtration Problem in the Presence of a Point Source,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 1, 58–63 (2005) [Russian Mathematics (Iz. VUZ) 49, No. 1, 53–59 (2005)].

  9. V. D. Glushenkov, “One Equation of Nonlinear Filtration Theory,” in Prikl. Matem. v Tekhniko-Ekonomicheskikh Zadachakh, (Kazansk. Gos. Univ., Kazan, 1976), pp. 12–21.

    Google Scholar 

  10. G. I. Bernadiner and V. M. Entov, Hydrodynamic Theory of Seepage Flow of Anomalous Fluids (Nauka, Moscow, 1975) [in Russian].

    Google Scholar 

  11. R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis (North-Holland Publ. Co., Amsterdam, 1979; Mir, Moscow, 1981).

    MATH  Google Scholar 

  12. Ph. Ciarlet, The Finite Element Method for Elliptic Problems (North-Holland Publ. Co., Amsterdam-New York, 1978; Mir, Moscow, 1980).

    MATH  Google Scholar 

  13. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods (Springer Series in Comp. Math., 1991).

  14. J.-L. Lions, Problèmes aux Limites Non Homogenes et Applications (Dunod, Paris, 1968; Mir, Moscow, 1972).

    MATH  Google Scholar 

  15. M. M. Karchevskii and A. V. Lapin, “Investigation of the Difference Scheme for a Nonlinear Stationary Problem of Filtration Theory,” Issled. po Prikladnoi Matem., Kazansk. Gos. Univ., Kazan, No. 6, 23–31 (1979).

  16. L. V. Maslovskaya, “A Generalized Cholesky Algorithm for Mixed Discrete Analogues of Elliptic Boundary-Value Problems,” Zhurn. Vychisl. Matem. i Matem. Fiz. 29(1), 67–74 (1989).

    MATH  MathSciNet  Google Scholar 

  17. L. V. Maslovskaya, “Conditions of Applicability of the Generalized Cholesky Algorithm,” Zhurn. Vychisl. Matem. i Matem. Fiz. 32(3), 339–347 (1992).

    MathSciNet  Google Scholar 

  18. Kh. D. Ikramov, “Some Comments on the Generalized Cholesky Algorithm,” Zhurn. Vychisl. Matem. i Matem. Fiz. 32(7), 1126–1130 (1992).

    MATH  MathSciNet  Google Scholar 

  19. E. G. D’yakonov, Minimization of Computation Costs. Asymptotically Optimal Algorithms for Elliptic Problems (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  20. E. V. Chizhonkov, “Relaxation Solution Methods for Equations with Saddle Operators,” in Iteratsionnye Metody Resheniya Lineinykh i Nelineinykh Setochnykh Zadach (N. I. Lobachevskii Math. Center, 1999), Vol. 2, pp. 44–93.

    Google Scholar 

  21. M. M. Karchevskii and A. D. Lyashko, Difference Schemes for Nonlinear Equations of Mathematical Physics (Kazansk. Gos. Univ., Kazan, 1976) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to O. A. Zadvornov.

Additional information

Original Russian Text © O.A. Zadvornov, M.M. Karchevskii, A.E. Fedotov, 2007, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2007, No. 8, pp. 16–26.

About this article

Cite this article

Zadvornov, O.A., Karchevskii, M.M. & Fedotov, A.E. Application of mixed schemes of the finite element method to the solution of problems of nonlinear filtration theory. Russ Math. 51, 14–24 (2007). https://doi.org/10.3103/S1066369X07080026

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X07080026

Keywords

Navigation