Abstract
We extend the classical Céa-Falk Lemma to variational inequalities of the second kind defined by strongly monotone operators. As an application we derive an asymptotic error estimate for an obstacle problem with a friction
References
- R. Adams: Sobolev Spaces, Academic Press, New York (1975).Google Scholar
- H. W. Alt: Lineare Funktionalanalysis, Springer, Berlin (1999).https://doi.org/10.1007/978-3-662-08387-1Google Scholar
- S. Brenner, R. Scott: The Mathematical Theory of Finite Element Methods, Springer, New York (1994).https://doi.org/10.1007/978-1-4757-4338-8Google Scholar
- C. Carstensen, J. Gwinner: FEM and BEM coupling for a nonlinear transmission problem with Signorini contact, SIAM J. Numer. Anal. 34 (1997) 1845–1864.https://doi.org/10.1137/S0036142995281139Google Scholar
- J. Céa: Approximation variationnelle des problémes aux limites, Ann. Inst. Fourier 14 (1964) 345–444.https://doi.org/10.5802/aif.181Google Scholar
- P. G. Ciarlet: The Finite Element Methods for Elliptic Problems, North-Holland, Amsterdam (1978).https://doi.org/10.1115/1.3424474Google Scholar
- P. G. Ciarlet, J. L. Lions: Handbook of Numerical Analysis, Vol. II, North-Holland, Amsterdam (1991).Google Scholar
- R. S. Falk: Error estimates for the approximation of a class of variational inequalities, Math. Comput. 28 (1974) 963–971.https://doi.org/10.1090/S0025-5718-1974-0391502-8Google Scholar
- I. Ekeland, R. Témam: Convex Analysis and Variational Problems, North-Holland, Amsterdam (1976).Google Scholar
- R. Glowinski: Numerical Methods for Nonlinear Variational Problems, Springer, New York (1984).https://doi.org/10.1007/978-3-662-12613-4Google Scholar
- R. Glowinski, J. L. Lions, R. Trémoliéres: Numerical Analysis of Variational Inequalities, North-Holland, Amsterdam (1981).Google Scholar
- R. Glowinski, A. Marrocco: Sur l’approximation, par éléments finis d’ordre un, et la résolution, par pénalisation-dualité d’une classe de probèmes de Dirichlet non linéaires, Rev. Franc. Automat. Inform. Rech. Operat. 9 (1975) 41–76.https://doi.org/10.1051/m2an/197509R200411Google Scholar
- J. Gwinner: Finite element convergence for contact problems in plane linear elastostatics, Q. Appl. Math. 50(1) (1992) 11–25.https://doi.org/10.1090/qam/1146620Google Scholar
- J. Gwinner: Céa’s error estimate for strongly monotone variational inequalities, Appl. Anal. 45 (1992) 179–192.https://doi.org/10.1080/00036819208840094Google Scholar
- H. Jeggle: Nichtlineare Funktionalanalysis, B. G. Teubner, Stuttgart (1979).https://doi.org/10.1007/978-3-322-94888-5Google Scholar
- D. Kinderlehrer, G. Stampacchia: An Introduction to Variational Inequalities and their Applications, Academic Press, New York (1980).Google Scholar
- M. Ružička: Nichtlineare Funktionalanalysis, Springer, Berlin (2004).Google Scholar
- E. Zeidler: Nonlinear Functional Analysis and its Applications. II/A: Linear Monotone Operators, Springer, New York (1990).https://doi.org/10.1007/978-1-4612-0985-0Google Scholar
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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.
