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An up-wind finite element method for a filtration problem. (English) Zbl 0506.76095


MSC:

76S05 Flows in porous media; filtration; seepage
76M99 Basic methods in fluid mechanics
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Citations:

Zbl 0392.76091
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References:

[1] H W ALT, Stromungen durch inhomogene porose Medien mit freiem Rand, J Reine Angew Math 305 (1979), 89-115 Zbl0392.76091 MR518852 · Zbl 0392.76091
[2] H W ALT, Numerical solution of steady-state porous flow free boundary problems, Numer Math 36 (1980), 73-98 Zbl0447.76074 MR595808 · Zbl 0447.76074
[3] H W ALT, G GILARDI, The behavior of the free boundary for the dam problem, to appear Zbl0521.76092 · 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 Zbl0258.76069 MR408443 · 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 Zbl0317.49009 MR399982 · 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 · Zbl 1308.49002
[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 Zbl0296.76052 MR329288 · 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 Zbl0343.76036 MR342026 · 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) Zbl0391.76072 · 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 · Zbl 0462.76090
[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 Zbl0251.65069 · 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 Zbl0217.21903 · Zbl 0217.21903
[15] R FALK, Error estimates for the approximation of a class of variational inequalities, Math Comp 28 (1974), 963-971 Zbl0297.65061 · Zbl 0297.65061
[16] R GLOWINSKI, J L LIONS, R TREMOLIERES, Analyse numérique des inéquations variationnelles, Vol 1, 2 (1976), Dunod, Paris Zbl0358.65091 · Zbl 0358.65091
[17] M MUSKAT, The flow of homogeneous fluids through porous media (1937), McGraw-Hill, New York JFM63.1368.03 · 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 Zbl0391.65038 MR495024 · Zbl 0391.65038
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