Mixed formulations for a class of variational inequalities

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1. D.A. Adams, Sobolev spaces. Academic Press, New York (1975).  
2. L. Baillet and T. Sassi, Méthode d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottement. C.R. Acad. Sciences Paris Série I334 (2002) 917–922.  
3. F. Ben Belgacem, Y. Renard and L. Slimane, A mixed formulation for the Signorini problem in incompressible elasticity, theory and finite element approximation. Appl. Numer. Math. (to appear).  
4. H. Brezis, Analyse fonctionnelle : Théorie et applications. Masson, Paris (1983).  
5. F. Brezzi and M. Fortin, Mixed and hybrid finite element methods. Springer-Verlag, Berlin (1991).  
6. F. Brezzi, W. Hager and P.A. Raviart, Error estimates for the finite element solution of variational inequalities, Part II. Numer. Math31 (1978) 1–16.  
7. D. Capatina-Papaghiuc, Contribution à la prévention de phénomènes de verrouillage numérique. Ph.D. thesis, Université de Pau, France (1997).  
8. D. Capatina-Papaghiuc and N. Raynaud, Numerical approximation of stiff transmission problems by mixed finite element methods. RAIRO Modél. Math. Anal. Numér.32 (1998) 611–629.  
9. P.G. Ciarlet, The finite element methods for elliptic problems. North-Holland, Amsterdam (1978).  
10. P. Coorevits, P. Hild, K. Lhalouani and T. Sassi, Mixed finite elemen methods for unilateral problems: convergence analysis and numerical studies. Math. Comp.71(2001) 1–25.  
11. G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique. Dunod, Paris (1972).  
12. I. Ekeland and R. Temam, Analyse convexe et problèmes variationnels. Dunod, Paris (1974).  
13. R.C. Falk, Error estimates for the approximation of a class of variational inequalities. Math. Comp.28 (1974) 863–971.  
14. J. Haslinger, Mixed formulation of elliptic variational inequalities and its approximation. Appl. Math.6 (1981) 462–475.  
15. J. Haslinger, I. Hlaváček and J. Nečas, Numerical methods for unilateral problems in solid mechanics. Handb. Numer. Anal., Vol. IV: Finite Element Methods, Part 2 – Numerical Methods for solids, Part 2, P.G. Ciarlet and J.-L. Lions Eds., North-Holland, Amsterdam (1996).  
16. J. Jarušek, Contact problems with bounded friction, coercive case. Czech. Math. J.33 (1983) 237–261.  
17. N. Kikuchi and J.T. Oden, Contact problems in elasticity: A Study of variational Inequalities and Finite Element Methods. SIAM, Philadelphia (1988).  
18. K. Lhalouani and T. Sassi, Nonconforming mixed variational formulation and domain decomposition for unilateral problems. East-West J. Num. Math.7 (1999) 23–30.  
19. J.-L. Lions, Quelques méthodes de résolution de problème aux limites non linéaires. Dunod, Paris (1969).  
20. U. Mosco, Convergence of convex sets and of solutions of variational inequalities. Adv. Math.3 (1969) 510–585.  
21. M. Moussaoui and K. Khodja, Régularité des solutions d'un problème mêlé Dirichlet-Signorini dans un domaine polygonal plan. Comm. Partial Differential Equations17 (1992) 805–826.  
22. N. Raynaud, Approximation par méthode d'éléments finis de problèmes de transmission raides. Ph.D. thesis, Université de Pau, France (1994).  
23. J.E. Robert and J.-M. Thomas, Mixed and Hybrid Methods. Handb. Numer. Anal., Vol. II: Finite Element Methods, Part 1, North-Holland, Amesterdam (1991).  
24. L. Slimane, Méthodes mixtes et traitement du verrouillage numérique pour la résolution des inéquations variationnelles. Ph.D. thesis, INSA de Toulouse, France (2001).  
25. L. Slimane, A. Bendali and P. Laborde, Mixed formulations for a class of variational inequalities.C.R. Math. Acad. Sci. Paris334 (2002) 87–92.  
26. L. Wang and G. Wang, Dual mixed finite element method for contact problem in elasticity. Math. Num. Sin. 21 (1999).  

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