Abstract
In this paper we study the convergence of a finite element approximation for a variational inequality related to hydraulics and we prove, for both linear and quadratic elements, error bounds in terms of the mesh size and a theorem of convergence of the domains
Similar content being viewed by others
References
J. P. Aubin,Approximation of elliptic boundary value problems (1972), Wiley-Interscience, New York.
C. Baiocchi,Sur quelques problèmes à frontière libre, Colloque International C.N.R.S. sur les équations aux dérivées partielles linéaires, Orsay, 1973.
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.
C. Baiocchi—G. A. Pozzi, to appear.
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.
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.
J. Bear,Dynamics of fluids in porous media (1972), American Elsevier, New York.
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.
P. G. Ciarlet—P. A. Raviart,La méthode des elements finis pour les problèmes aux limites élliptiques, book to appear.
R. Falk,Error estimates for the approximation of a class of variational inequalities, Math. Comp. 28 (1974), 963–971.
M. E. Haar,Groundwater and seepage (1972), Mac Graw Hill, New York.
J. L. Lions,Problèmes aux limites dans les équations aux dérivées partielles (1965), Les Presses de l’Université, Montréal.
J. L. Lions—G. Stampacchia,Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493–519.
U. Mosco—G. Strang,One-sided approximation and variational inequalities, to appear on Bull. Amer. Soc.
M. Muskat,The flow of homogeneous fluids through porous media (1973), Mac Graw Hill, New York.
J. A. Nitsche,L ∞-convergence of finite element approximation, Proceedings of 2d conference of Finite Elements, Rennes, France, 1975.
P. A. Raviart,Méthode des elements finis (1972), Université Paris VI et C.N.R.S., Paris.
G. Strang—G. J. Fix,An analysis of the finite element method (1973), Prentice Hall, New York.
G. Strang,Finite elements and variational inequalities, Analisi Convessa e Applicazioni, Proceedings of Giornate di Analisi Convessa e Applicazioni, Roma, 1974.
Author information
Authors and Affiliations
Additional information
This work is based in part on the graduation thesis of G. Sacchi discussed in october 1974 at University of Pavia.
Rights and permissions
About this article
Cite this article
Brezzi, F., Sacchi, G. A finite element approximation of a variational inequality related to hydraulics. Calcolo 13, 257–273 (1976). https://doi.org/10.1007/BF02575934
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02575934