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A finite element approximation of a variational inequality related to hydraulics. (English) Zbl 0353.76068

MSC:
76S05Flows in porous media; filtration; seepage
References:
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[2]C. Baiocchi,Sur quelques problèmes à frontière libre, Colloque International C.N.R.S. sur les équations aux dérivées partielles linéaires, Orsay, 1973.
[3]C. Baiocchi,Sa un problema di frontiera libera connesso a questioni di idraulica, Ann. Mat. Pura Appl. (IV) XCII (1972), 107–127; C. R. Acad. Sc Paris, 273 (1971), 1215–1217.
[4]C. Baiocchi–G. A. Pozzi, to appear.
[5]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. · Zbl 0296.76052 · doi:10.1007/BF02576418
[6]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. (IV) XCVII (1973) 1–82.
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[9]P. G. Ciarlet–P. A. Raviart,La méthode des elements finis pour les problèmes aux limites élliptiques, book to appear.
[10]R. Falk,Error estimates for the approximation of a class of variational inequalities, Math. Comp. 28 (1974), 963–971. · doi:10.1090/S0025-5718-1974-0391502-8
[11]M. E. Haar,Groundwater and seepage (1972), Mac Graw Hill, New York.
[12]J. L. Lions,Problèmes aux limites dans les équations aux dérivées partielles (1965), Les Presses de l’Université, Montréal.
[13]J. L. Lions–G. Stampacchia,Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493–519. · Zbl 0152.34601 · doi:10.1002/cpa.3160200302
[14]U. Mosco–G. Strang,One-sided approximation and variational inequalities, to appear on Bull. Amer. Soc.
[15]M. Muskat,The flow of homogeneous fluids through porous media (1973), Mac Graw Hill, New York.
[16]J. A. Nitsche,L convergence of finite element approximation, Proceedings of 2 d conference of Finite Elements, Rennes, France, 1975.
[17]P. A. Raviart,Méthode des elements finis (1972), Université Paris VI et C.N.R.S., Paris.
[18]G. Strang–G. J. Fix,An analysis of the finite element method (1973), Prentice Hall, New York.
[19]G. Strang,Finite elements and variational inequalities, Analisi Convessa e Applicazioni, Proceedings of Giornate di Analisi Convessa e Applicazioni, Roma, 1974.