Mixed finite element approximation of 3D contact problems with given friction: Error analysis and numerical realization

Mathematical Modelling and Numerical Analysis

Volumn 38, Issue 3, 2004, Pages 563-578

  Haslinger, Jaroslav ^a   Sassi, Taoufik ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b CNRS   (France)

Author keywords

A priori error estimates; Mixed finite element methods; Unilateral contact problems with friction

Indexed keywords

EID: 3142718395     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2004026     Document Type: Article

References (19)

1. R.A. Adams, Sobolev Spaces. Academic Press (1975).
2. G. Amontons, Sur l'origine de la résistance dans les machines. Mémoires de l'Académie Royale (1699) 206-222.
3. L. Baillet and T. Sassi, Méthodes d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottement, C.R. Acad. Sci. Paris, Ser. I 334 (2002) 917-922.
4. G. Bayada, M. Chambat, K. Lhalouani and T. Sassi. Éléments finis avec joints pour des problèmes de contact avec frottement de Coulomb non local. C.R. Acad. Sci. Paris, Ser. I 325 (1997) 1323-1328.
5. P.-G. Ciarlet, The finite element method for elliptic problems, Handbook of Numerical Analysis. P.G. Ciarlet and J.L. Lions Eds., Vol. 2, Part 1, North-Holland (1991) 17-352.
6. C.A. Coulomb, Théorie des machines simples. Mémoire de Mathématique et de Physique de l'Académie Royale 10 (1785) 145-173.
7. Z. Dostál, Box constrained quadratic programming with proportioning and projections. SIAM J. Opt. 7 (1997) 871-887.
8. G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique. Dunod, Paris (1972).
9. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland, Amsterdam (1976).
10. R. Glowinski, Numerical methods for nonlinear variational problems. Springer, New York (1984).
11. P. Grisvard, Elliptic Problems in Nonsmooth Domains. Monogr. Studies Math., Pitman 24 (1985).
12. J. Haslinger and I. Hlaváček, Approximation of the Signorini problem with friction by mixed finite element method, J. Math. Anal. Appl. 86 (1982) 99-122.
13. J. Haslinger and P.D. Panagiolopoulas, Approximation of contact problems with friction by reciprocal variational formulations. Proc. Roy. Soc. Edinburgh 98A (1984) 365-383.
14. J. Haslinger, I. Hlaváček and J. Nečas, Numerical methods for unilateral problems in solid mechanics, Handbook of Numerical Analysis, P.G. Ciarlet and J.L. Lions Eds., Vol. 4, Part 2, North-Holland (1996) 313-485.
15. J. Haslinger, R. Kučera and Z. Dostál, An algorithm for numerical realization of 3D contact problems with Coulomb friction. J. Comput. Appl. Math. 164-165 (2004) 387-408.
16. P. Hild, À propos d'approximation par éléments finis optimale pour les problèmes de contact unilatéral. C.R. Acad. Sci. Paris, Ser. 1326 (1998) 1233-1236.
17. N. Kikuchi and J.T. Oden, Contact problems in elasticity: a study of variational inequalities and finite element methods. SIAM, Philadelphia (1988).
18. D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications. Academic Press (1980).
19. K. Lhalouani and T. Sassi, Nonconforming mixed variational formulation and domain decomposition for unilateral problems. East-West J. Numer. Math. 7 (1999) 23-30.