An up-wind finite element method for a filtration problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 16 (1982) no. 4, p. 463-481
@article{M2AN_1982__16_4_463_0,
     author = {Pietra, P.},
     title = {An up-wind finite element method for a filtration problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {16},
     number = {4},
     year = {1982},
     pages = {463-481},
     zbl = {0506.76095},
     mrnumber = {684833},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1982__16_4_463_0}
}
Pietra, P. An up-wind finite element method for a filtration problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 16 (1982) no. 4, pp. 463-481. http://www.numdam.org/item/M2AN_1982__16_4_463_0/

[1] H W Alt, Stromungen durch inhomogene porose Medien mit freiem Rand, J Reine Angew Math 305 (1979), 89-115 | MR 518852 | Zbl 0392.76091

[2] H W Alt, Numerical solution of steady-state porous flow free boundary problems, Numer Math 36 (1980), 73-98 | MR 595808 | Zbl 0447.76074

[3] H W Alt, G Gilardi, The behavior of the free boundary for the dam problem, to appear | Numdam | Zbl 0521.76092

[4] C Baiocchi, Su un problema di frontiera libera connesso a questioni di idraulica, Ann Mat Pura Appl (4) 92 (1972), 107-127 | MR 408443 | Zbl 0258.76069

[5] C Baiocchi, Studio di un problema quasi-variazionale connesso a problemi di frontiera libera, Boll U M I (4) 11 (Suppl fasc 3) (1975), 589-631 | MR 399982 | Zbl 0317.49009

[6] C Baiocchi, A Capelo, Disequazioni variazionai e quasi-variazionali Applicazioni a problemi di frontiera libera, Vol 1, 2 (1978), Pitagora Editrice, Bologna

[7] C Baiocchi, V Comincioli, L Guerri, G Volpi, Free boundary problems in the theory of fluid flow through porous media a numerical approach, Calcolo 10 (1973), 1-86 | MR 329288 | Zbl 0296.76052

[8] C Baiocchi, V Comincioli, E Magenes, G A Pozzi, Free boundary problems in the theory of fluid flow through porous media existence and uniqueness theorems, Ann Mat Pura Appl (4) 97 (1973), 1-82 | MR 342026 | Zbl 0343.76036

[9] J Bear, Dynamics of fluids in porous media (1972), American Elsevier, New York | Zbl 1191.76001

[10] H Brezis, D Kinderleherer, G Stampacchia, Sur une nouvelle formulation du problème de l'écoulement à travers une digue, C R Acad Sc Paris (1978) | Zbl 0391.76072

[11] F Brezzi, G Sacchi, A finite approximation for solving the dam problem, Calcolo 13 (1976), 257-273 | Zbl 0353.76068

[12] M Chipot, Problème de l'écoulement à travers une digue (1981), Doctorat d'Etat, Université Pierre et Marie Curie, Paris

[13] P G Ciarlet, P A Raviart, Maximum principle and uniform convergence for the finite element method, Comput Methods Appl Engrg 2 (1973), 17-31 | Zbl 0251.65069

[14] C W Cryer, On the approximate solution of free boundary problems using finite differences, J Assoc Comput Mach 17 (1970), 397-411 | Zbl 0217.21903

[15] R Falk, Error estimates for the approximation of a class of variational inequalities, Math Comp 28 (1974), 963-971 | Zbl 0297.65061

[16] R Glowinski, J L Lions, R Tremolieres, Analyse numérique des inéquations variationnelles, Vol 1, 2 (1976), Dunod, Paris | Zbl 0358.65091

[17] M Muskat, The flow of homogeneous fluids through porous media (1937), McGraw-Hill, New York | JFM 63.1368.03

[18] P A Raviart, Approximation numérique des phénomènes de diffusion-convection (1979), Ecole d'été d'analyse numérique, C E A, E D F, I R I A

[19] M Tabata, Uniform convergence of the up-wind finite element approximation for semilinear parabolic problems, J Math , Kyoto Univ 18 (1978), 327-351 | MR 495024 | Zbl 0391.65038