×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI EuDML
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.