50
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Analysis of Galerkin-characteristics algorithm for variably saturated flow in porous media

Pages 509-525 | Received 05 Mar 2007, Accepted 21 Mar 2007, Published online: 22 Sep 2010

References

  • Sorek , S. and Braester , C. An adaptive Eulerian-Lagrangian approach for the numerical simulation of unsaturated flow . Proceedings of the 6th International Conference on Finite Elements in Water Resources . 1986 . New York : Springer Verlag .
  • van Genuchten , M. T. 1980 . A closed-form equation for predicting the hydraulic conductivity of unsaturated soils . Soil Science Society of America Journal , 44 : 892 – 898 .
  • Mualem , Y. 1976 . A new model predicting the hydraulic conductivity of unsaturated porous media . Water Resource Research , 12 : 513 – 522 .
  • Schaap , M. G. and Leij , F. J. 2000 . Improved prediction of unsaturated hydraulic conductivity with the Mualem-van Genuchten . Soil Science Society of America Journal , 64 : 843 – 851 .
  • Jäger , W. and Kaĉur , J. 1991 . Solution of porous medium systems by linear approximation scheme . Numerical Mathematics , 60 : 407 – 427 .
  • Jäger , W. and Kaĉur , J. 1995 . Solution of doubly nonlinear and degenerate parabolic problems by relaxation schemes . M2AN Mathematical Modeling and Numerical Analysis , 29 : 605 – 627 .
  • Kaĉur , J. 1996 . Solution to strongly nonlinear parabolic problems by a linear approximation scheme . IMA Journal of Numerical Analysis , 19 : 1 – 26 .
  • Slodiĉka , M. 2002 . A robust and efficient linearization scheme for doubly nonlinear and degenerate parabolic problems arising in flow in porous media . SIAM Journal on Scientific Computing , 23 : 1593 – 1614 .
  • Douglas , J. and Russell , T. F. 1982 . Numerical methods for convection dominated diffusion problems based on combining the method of the characteristics with finite elements or finite differences . SIAM Journal on Numerical Analysis , 19 : 871 – 885 .
  • Pironneau , O. 1982 . On the transport-diffusion algorithm and its applications to the Naiver–Stokes equations . Numerical Mathematics , 38 : 309 – 332 .
  • Morton , K. W. , Priestley , A. and Süli , E. 1988 . Convergence of the Lagrange-Galerkin method with non-exact integration . M2AN Mathematical Modeling and Numerical Analysis , 22 : 625 – 653 .
  • Bermejo , R. 1995 . A Galerkin-Characteristics algorithm for transport-diffusion equation . SIAM Journal on Numerical Analysis , 32 : 425 – 455 .
  • Mahmood , M. Sh. 2000 . “ The regularized Galerkin characteristics algorithm for contaminant transport with equilibrium and non-equilibrium adsorption ” . Comenius University . PhD thesis
  • Dawson , C. N. 1998 . Analysis of an upwind-mixed finite element method for nonlinear contaminant transport equation . SIAM Journal on Numerical Analysis , 5 : 1709 – 1725 .
  • Douglas , J. , Huang , C.-S. and Pereira , F. 1999 . The modified method of characteristics with adjusted advection . Numerical Mathematics , 83 : 353 – 369 .
  • Douglas , J. , Pereira , F. and Yeh , Li-M. 2000 . A locally conservative Eulerian-Lagrangian numerical method and its application to nonlinear transport in porous media . Computational Geosciences , 4 ( 1 ) : 1 – 40 .
  • Arbogast , T. and Huang , C.-S. 2005 . “ A full mass and volume conserving implementation of a characteristic method for transport problems ” . 05-08 ICES Report
  • Arbogast , T. and Wheeler , M. F. 1995 . A characteristics-mixed finite element method for advection dominated transport problems . SIAM Journal on Numerical Analysis , 32 : 404 – 424 .
  • Mahmood , M. Sh. Solution of strongly nonlinear convection-diffusion problems by a conservative Galerkin-characteristics method . Numerische Mathematika , to appear
  • Douglas , J , Furtado , F. and Pereira , F. 1997 . On the numerical simulation of water flooding of heterogeneous petroleum resevoirs . Computational Geosciences , 1 : 155 – 190 .
  • Kaĉur , J. 2001 . Solution of degenerate convection-diffusion problems by the method of characteristics . SIAM Journal on Numerical Analysis , 39 : 858 – 879 .
  • Kaĉur , J. and Mahmood , M. Sh. 2003 . Solution of Solute transport in unsaturated porous media by the method of characteristics . Numerical Methods for Partial Differential Equations , 19 : 732 – 761 .
  • Kaĉur , J. and Mahmood , M. Sh. Solution of convection-diffusion problems with memory terms by the method of characteristics . Submitted
  • Kufner , A. , John , O. and Fuĉ´ik , S. 1977 . Function spaces , Leiden : Noordhoff .
  • Alt , H. W. and Luckhaus , S. 1983 . Quasilinear elliptic-parabolic differential equations . Mathematische Zeitschrift , 183 : 311 – 341 .
  • Feistauer , M. 1993 . “ Pitman monographs and surveys in pure and applied mathematics ” . In Mathematical Methods in Fluid Dynamics , Vol. 7 , Harlow : Longman Scientific & Technical .
  • Kaĉur , J. 1985 . Method of Rothe in evolution equations . Teubner-Texte zur Mathematic , 80, Leipzig
  • Simos , T. E. and Vigo-Aguiar , J. 2000 . A new modified Runge-Kutta-Nystrom method with phase-lag of order infinity for the numerical solution of the Schrodinger equation and related problems . International Journal of Modern Physics , 11 : 1195 – 1208 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.