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


76S05 Flows in porous media; filtration; seepage
Full Text: DOI


[1] J. P. Aubin,Approximation of elliptic boundary value problems (1972), Wiley-Interscience, New York. · Zbl 0248.65063
[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. · Zbl 0258.76069
[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
[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. · Zbl 0343.76036
[7] J. Bear,Dynamics of fluids in porous media (1972), American Elsevier, New York. · Zbl 1191.76001
[8] P. G. Ciarlet–P. A. Raviart,General Lagrange and Hermite interpolation in R n with applications to finite elements method, Arch. Rat. Mech. Anal. 46 (1972), 177–189. · Zbl 0243.41004
[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. · Zbl 0297.65061
[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
[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. · Zbl 0278.65116
[19] G. Strang,Finite elements and variational inequalities, Analisi Convessa e Applicazioni, Proceedings of Giornate di Analisi Convessa e Applicazioni, Roma, 1974.
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.