A priori error estimates for a mixed finite element discretization of the Richards' equation

Numerische Mathematik

Volumn 98, Issue 2, 2004, Pages 353-370

  Schneid, Eckhard ^a   Knabner, Peter ^a   Radu, Florin ^a  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4544359059     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-003-0509-2     Document Type: Article

References (12)

1. Alt, H.W., Luckhaus, S.: Quasilinear elliptic-parabolic equations. Math. Z. 183, 311-341 (1983)
2. Arbogast, T., Wheeler, M.F., Nai-Ying Zhang: A nonlinear mixed finite element method for a degenerate parabolic equation arising in flow in porous media. SIAM J. Numer. Anal. 33, 1669-1687 (1996)
3. Bastian, P., Birken, K., Johanssen, K., Lang, S., Neuß, N., Rentz-Reichert, H., Wieners, C.: UG-a flexible toolbox for solving partial differential equations. Comput. Visualiz. Sci. 1, 27-40 (1997)
4. Brezzi, F., Fortin, M.: Mixed and hybrid finite element methods. Springer Verlag, New York, 1991
5. Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978
6. Dautray, R., Lions, J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology. Volume 5, Evolution Problems I. Springer, Berlin, 1992
7. Nochetto, R.H., Verdi, C.: Approximation of degenerate parabolic problems using numerical integration. SIAM J. Numer. Anal. 25, 784-814 (1988)
8. Quarteroni, A., Valli, A.: Numerical Approximation of Partial Differential Equations. Springer Verlag, Berlin-Heidelberg, 1994
9. Radu, F., Pop, I.S., Knabner, P.: Error estimates for an Euler implicit, mixed finite element discretization of Richards' equation: equivalence between mixed and conformal approaches. Accepted for publication in (2003) SIAM J. Numer. Anal.
10. San Soucie, C.A.: Mixed finite element methods for variably saturated subsurface flow. PhD thesis, Texas Institute for Computational and Applied Mathematics, University of Austin, May 1996
11. Schneid, E.: Hybrid-Gemischte Finite-Elemente-Diskretisierung der Richards-Gleichung (in German). Ph.D. thesis, University of Erlangen- Nürnberg, 2000. Also available at http://www.am.uni-erlangen.de/am1/ publications/dipl_phd_thesis/dipl_phd_thesis.html
12. 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(3), 701-724 (2000)