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Volumn 168, Issue 1-2, 2004, Pages 365-373

Mixed finite elements for the Richards' equation: Linearization procedure

Author keywords

Degenerate parabolic problems; Euler implicit scheme; Linearization; Mixed finite elements; Regularization; Richards' equation

Indexed keywords

ITERATIVE METHODS; LINEARIZATION; NONLINEAR SYSTEMS; PROBLEM SOLVING;

EID: 2942522387     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.04.008     Document Type: Article
Times cited : (163)

References (25)
  • 1
    • 0000836987 scopus 로고
    • Quasilinear elliptic-parabolic differential equations
    • Alt H.W. Luckhaus S. Quasilinear elliptic-parabolic differential equations Math. Z. 183 1983 311-341
    • (1983) Math. Z. , vol.183 , pp. 311-341
    • Alt, H.W.1    Luckhaus, S.2
  • 2
    • 0000325197 scopus 로고    scopus 로고
    • A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media
    • Arbogast T. Wheeler M.F. Zhang N.Y. A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media SIAM J. Numer. Anal. 33 1996 1669-1687
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1669-1687
    • Arbogast, T.1    Wheeler, M.F.2    Zhang, N.Y.3
  • 3
    • 69949101897 scopus 로고    scopus 로고
    • UG-a flexible toolbox for solving partial differential equations
    • Bastian P. et-al UG-a flexible toolbox for solving partial differential equations Comput. Visualization Sci. 1 1997 27-40
    • (1997) Comput. Visualization Sci. , vol.1 , pp. 27-40
    • Bastian, P.1
  • 6
    • 0025585761 scopus 로고
    • A general mass-conservative numerical solution for the unsaturated flow equation
    • Celia M.A. Bouloutas E.T. Zarba R.L. A general mass-conservative numerical solution for the unsaturated flow equation Water Resource Res. 26 1990 1483-1496
    • (1990) Water Resource Res. , vol.26 , pp. 1483-1496
    • Celia, M.A.1    Bouloutas, E.T.2    Zarba, R.L.3
  • 7
    • 34250248086 scopus 로고
    • Nonstationary filtration in partially saturated porous media
    • van Duijn C.J. Peletier L.A. Nonstationary filtration in partially saturated porous media Arch Rational Mech. Anal. 78 1982 173-198
    • (1982) Arch Rational Mech. Anal. , vol.78 , pp. 173-198
    • van Duijn, C.J.1    Peletier, L.A.2
  • 8
    • 0033513105 scopus 로고    scopus 로고
    • The finite volume method for Richards equation
    • Eymard R. Gutnic M. Hillhorst D. The finite volume method for Richards equation Comput. Geosci. 3 1999 259-294
    • (1999) Comput. Geosci. , vol.3 , pp. 259-294
    • Eymard, R.1    Gutnic, M.2    Hillhorst, D.3
  • 10
    • 0000523964 scopus 로고
    • Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes
    • Jäger W. Kačur J. Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes M2AN Math. Model. Numer. Anal. 29 1995 605-627
    • (1995) M2AN Math. Model. Numer. Anal. , vol.29 , pp. 605-627
    • Jäger, W.1    Kačur, J.2
  • 11
    • 2342451866 scopus 로고    scopus 로고
    • Numerical solution of unsteady saturated/unsaturated flow through porous media
    • M. Feistauer, et al. (Eds.), Matfyzpress, Prague
    • P. Knabner, E. Schneid, Numerical solution of unsteady saturated/unsaturated flow through porous media, in: M. Feistauer, et al. (Eds.), Numerical Modelling in Continuum Mechanics, Part II, Matfyzpress, Prague, 1997, pp. 337-343.
    • (1997) Numerical Modelling in Continuum Mechanics , Issue.PART 2 , pp. 337-343
    • Knabner, P.1    Schneid, E.2
  • 12
    • 2942629179 scopus 로고    scopus 로고
    • Adaptive hybrid mixed finite element discretization of instationary variably saturated flow in porous media
    • M. Breuer, et al. (Eds.), Springer, Berlin
    • P. Knabner, E. Schneid, Adaptive hybrid mixed finite element discretization of instationary variably saturated flow in porous media, in: M. Breuer, et al. (Eds.), High Performance Scientific and Engineering Computing, Springer, Berlin, 2002, pp. 37-44.
    • (2002) High Performance Scientific and Engineering Computing , pp. 37-44
    • Knabner, P.1    Schneid, E.2
  • 13
    • 0001278368 scopus 로고
    • Approximation of degenerate parabolic problems using numerical integration
    • Nochetto R.H. Verdi C. Approximation of degenerate parabolic problems using numerical integration SIAM J. Numer. Anal. 25 1988 784-814
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 784-814
    • Nochetto, R.H.1    Verdi, C.2
  • 14
    • 0030579044 scopus 로고    scopus 로고
    • 1-contraction and uniqueness for quasilinear elliptic-parabolic equations
    • 1-contraction and uniqueness for quasilinear elliptic-parabolic equations J. Differential Equations 131 1996 20-38
    • (1996) J. Differential Equations , vol.131 , pp. 20-38
    • Otto, F.1
  • 16
    • 0036383180 scopus 로고    scopus 로고
    • Error estimates for a time discretization method for the Richards' equation
    • Pop I.S. Error estimates for a time discretization method for the Richards' equation Comput. Geosci. 6 2002 141-160
    • (2002) Comput. Geosci. , vol.6 , pp. 141-160
    • Pop, I.S.1
  • 17
    • 2942629407 scopus 로고    scopus 로고
    • On the existence and uniqueness of a solution for an elliptic problem
    • Pop I.S. Yong W.A. On the existence and uniqueness of a solution for an elliptic problem Studia Univ. Babes-Bolyai Math. 45 2000 97-107
    • (2000) Studia Univ. Babes-Bolyai Math. , vol.45 , pp. 97-107
    • Pop, I.S.1    Yong, W.A.2
  • 18
    • 0035982250 scopus 로고    scopus 로고
    • A numerical approach to degenerate parabolic equations
    • Pop I.S. Yong W.A. A numerical approach to degenerate parabolic equations Numer. Math. 92 2002 357-381
    • (2002) Numer. Math. , vol.92 , pp. 357-381
    • Pop, I.S.1    Yong, W.A.2
  • 19
    • 2942629180 scopus 로고    scopus 로고
    • Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards' equation
    • accepted for publication in SIAM
    • F. Radu, I.S. Pop, P. Knabner, Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards' equation, accepted for publication in SIAM J. Numer. Anal.
    • J. Numer. Anal.
    • Radu, F.1    Pop, I.S.2    Knabner, P.3
  • 21
    • 0036989014 scopus 로고    scopus 로고
    • A robust and efficient linearization scheme for doubly nonlinear and degenerate parabolic problems arising in flow in porous media
    • Slodicka M. A robust and efficient linearization scheme for doubly nonlinear and degenerate parabolic problems arising in flow in porous media SIAM J. Sci. Comput. 23 2002 1593-1614
    • (2002) SIAM J. Sci. Comput. , vol.23 , pp. 1593-1614
    • Slodicka, M.1
  • 24
    • 0001077416 scopus 로고    scopus 로고
    • Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media
    • Woodward C. Dawson C. Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media SIAM J. Numer. Anal. 37 2000 701-724
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 701-724
    • Woodward, C.1    Dawson, C.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.