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Volumn 42, Issue 4, 2004, Pages 1452-1478

Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards' equation

Author keywords

De generate parabolic problems; Error estimates; Euler implicit scheme; Mixed finite elements; Porous media; Regularization; Richards' equation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; EQUIVALENCE CLASSES; ERROR ANALYSIS; FINITE ELEMENT METHOD; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; POROUS MATERIALS;

EID: 25444508685     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142902405229     Document Type: Article
Times cited : (86)

References (30)
  • 1
    • 0000836987 scopus 로고
    • Quasilinear elliptic-parabolic differential equations
    • H. W. ALT AND S. LUCKHAUS, Quasilinear elliptic-parabolic differential equations, Math. Z., 183 (1983), pp. 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 inflow in porous media
    • T. ARBOGAST, M. F. WHEELER, AND N. Y. ZHANG, A nonlinear mixed finite element method for a degenerate parabolic equation arising inflow in porous media, SIAM J. Numer. Anal., 33 (1996), pp. 1669-1687.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1669-1687
    • Arbogast, T.1    Wheeler, M.F.2    Zhang, N.Y.3
  • 4
    • 0031105260 scopus 로고    scopus 로고
    • Mixed transform finite element method for solving the non-linear equation for flow in variably saturated porous media
    • R. G. BACA, J. N. CHUNG, AND D. J. MULLA, Mixed transform finite element method for solving the non-linear equation for flow in variably saturated porous media, Internat. J. Numer. Methods Fluids, 24 (1997), pp. 441-455.
    • (1997) Internat. J. Numer. Methods Fluids , vol.24 , pp. 441-455
    • Baca, R.G.1    Chung, J.N.2    Mulla, D.J.3
  • 6
    • 0033587522 scopus 로고    scopus 로고
    • Mixed finite elements and Newton-type linearizations for the solution of Richards' equation
    • L. BERGANASCHI AND M. PUTTI, Mixed finite elements and Newton-type linearizations for the solution of Richards' equation, Internat. J. Numer. Methods Engrg., 45 (1999), pp. 1025-1046.
    • (1999) Internat. J. Numer. Methods Engrg. , vol.45 , pp. 1025-1046
    • Berganaschi, L.1    Putti, M.2
  • 8
    • 0025585761 scopus 로고
    • A general mass-conservative numerical solution for the unsaturated flow equation
    • M. A. CELIA, E. T. BOULOUTAS, AND R. L. ZARBA, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res., 26 (1990), pp. 1483-1496.
    • (1990) Water Resour. Res. , vol.26 , pp. 1483-1496
    • Celia, M.A.1    Bouloutas, E.T.2    Zarba, R.L.3
  • 10
    • 0033513105 scopus 로고    scopus 로고
    • The finite volume method for Richards equation
    • R. EYMARD, M. GUTNIC, AND D. HILLHORST, The finite volume method for Richards equation, Comput. Geosci., 3 (1999), pp. 259-294.
    • (1999) Comput. Geosci. , vol.3 , pp. 259-294
    • Eymard, R.1    Gutnic, M.2    Hillhorst, D.3
  • 11
    • 0013016185 scopus 로고
    • A priori estimates and regularization for a class of porous medium equations
    • K. FADIMBA AND R. SHARPLEY, A priori estimates and regularization for a class of porous medium equations, Nonlinear World, 2 (1995), pp. 13-41.
    • (1995) Nonlinear World , vol.2 , pp. 13-41
    • Fadimba, K.1    Sharpley, R.2
  • 13
    • 0000523964 scopus 로고
    • Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes
    • W. JäGER AND J. KAČUR, Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes, RAIRO Model. Math. Numer. Anal., 29 (1995), pp. 605-627.
    • (1995) RAIRO Model. Math. Numer. Anal. , vol.29 , pp. 605-627
    • Jäger, W.1    Kačur, J.2
  • 14
    • 0035366337 scopus 로고    scopus 로고
    • Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards equation
    • D. KAVETSKI, P. BINNING, AND S. W. SLOAN, Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards equation, Adv. Water Res. 24 (2001), pp. 595-605.
    • (2001) Adv. Water Res. , vol.24 , pp. 595-605
    • Kavetski, D.1    Binning, P.2    Sloan, S.W.3
  • 15
    • 0742282613 scopus 로고
    • Finite element simulation of saturated-unsaturated flow through porous media
    • P. Deuflhard and B. Engquist, eds., Birkhäuser, Boston
    • P. KNABNER, Finite element simulation of saturated-unsaturated flow through porous media, in Large Scale Scientific Computing, Progress in Scientific Computing 7, P. Deuflhard and B. Engquist, eds., Birkhäuser, Boston, 1987, pp. 83-93.
    • (1987) Large Scale Scientific Computing, Progress in Scientific Computing , vol.7 , pp. 83-93
    • Knabner, P.1
  • 16
    • 2942629179 scopus 로고    scopus 로고
    • Adaptive hybrid mixed finite element discretization of instationary variably saturated flow in porous media
    • M. Breuer, F. Durst, and C. Zenger, eds., Springer-Verlag, Berlin
    • P. KNABNER AND E. SCHNEID, Adaptive hybrid mixed finite element discretization of instationary variably saturated flow in porous media, in High Performance Scientific and Engineering Computing, M. Breuer, F. Durst, and C. Zenger, eds., Springer-Verlag, Berlin, 2002, pp. 37-44.
    • (2002) High Performance Scientific and Engineering Computing , pp. 37-44
    • Knabner, P.1    Schneid, E.2
  • 17
    • 2342451866 scopus 로고    scopus 로고
    • Numerical solution of unsteady saturated/unsaturated flow through porous media
    • M. Feistauer, R. Rannacher, and K. Kozel, eds., Matfyzpress, Prague
    • P. KNABNER AND E. SCHNEID, Numerical solution of unsteady saturated/unsaturated flow through porous media, in Numerical Modelling in Continuum Mechanics, Part II, M. Feistauer, R. Rannacher, and K. Kozel, eds., Matfyzpress, Prague, 1997, pp. 337-343.
    • (1997) Numerical Modelling in Continuum Mechanics, Part II , pp. 337-343
    • Knabner, P.1    Schneid, E.2
  • 18
    • 25444459014 scopus 로고    scopus 로고
    • Efficient realization of the mixed finite element discretization for nonlinear problems
    • submitted
    • P. KNABNER AND G. SUMM, Efficient realization of the mixed finite element discretization for nonlinear problems, Math. Comp., submitted.
    • Math. Comp.
    • Knabner, P.1    Summ, G.2
  • 21
    • 0001278368 scopus 로고
    • Approximation of degenerate parabolic problems using numerical integration
    • R. H. NOCHETTO AND C. VERDI, Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer. Anal., 25 (1988), pp. 784-814.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 784-814
    • Nochetto, R.H.1    Verdi, C.2
  • 22
    • 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), pp. 20-38.
    • (1996) J. Differential Equations , vol.131 , pp. 20-38
    • Otto, F.1
  • 23
    • 0036383180 scopus 로고    scopus 로고
    • Error estimates for a time discretization method for the Richards' equation
    • I. S. POP, Error estimates for a time discretization method for the Richards' equation, Comput. Geosci., 6 (2002), pp. 141-160.
    • (2002) Comput. Geosci. , vol.6 , pp. 141-160
    • Pop, I.S.1
  • 24
    • 2942522387 scopus 로고    scopus 로고
    • Mixed finite elements for the Richards' equation: Linearization procedure
    • I. S. POP, F. RADU, AND P. KNABNER, Mixed finite elements for the Richards' equation: Linearization procedure, J. Comput. Appl. Math., 168 (2004), pp. 365-373.
    • (2004) J. Comput. Appl. Math. , vol.168 , pp. 365-373
    • Pop, I.S.1    Radu, F.2    Knabner, P.3
  • 26
    • 4544359059 scopus 로고    scopus 로고
    • A priori error estimates for a mixed finite element discretization of the Richards' equation
    • E. SCHNEID, P. KNABNER, AND F. RADU, A priori error estimates for a mixed finite element discretization of the Richards' equation, Numer. Math., 98 (2004), pp. 353-370.
    • (2004) Numer. Math. , vol.98 , pp. 353-370
    • Schneid, E.1    Knabner, P.2    Radu, F.3
  • 27
    • 84972508790 scopus 로고
    • An approach by difference to the porous medium equation with convection
    • M. WATANABE, An approach by difference to the porous medium equation with convection, Hiroshima Math. J., 25 (1995), pp. 623-645.
    • (1995) Hiroshima Math. J. , vol.25 , pp. 623-645
    • Watanabe, M.1
  • 28
    • 0033597588 scopus 로고    scopus 로고
    • An evaluation of temporally adaptive transformation approaches for solving Richards' equation
    • G. A. WILLIAMS AND C. T. MILLER, An evaluation of temporally adaptive transformation approaches for solving Richards' equation, Adv. Water Res. 22 (1999), pp. 831-840.
    • (1999) Adv. Water Res. , vol.22 , pp. 831-840
    • Williams, G.A.1    Miller, C.T.2
  • 29
    • 0001077416 scopus 로고    scopus 로고
    • Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media
    • C. WOODWARD AND C. DAWSON, 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), pp. 701-724.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 701-724
    • Woodward, C.1    Dawson, C.2
  • 30
    • 0031336891 scopus 로고    scopus 로고
    • A mixed finite element discretization on non-matching multiblock grids for a degenerate parabolic equation arizing in porous media flow
    • I. YOTOV, A mixed finite element discretization on non-matching multiblock grids for a degenerate parabolic equation arizing in porous media flow, East-West J. Numer. Math., 5 (1997), pp. 211-230.
    • (1997) East-west J. Numer. Math. , vol.5 , pp. 211-230
    • Yotov, I.1


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