Summary
In this paper the internal approximation of a quasi-variational inequality is considered. An algorithm of Bensoussan-Lions type is proposed for which the convergence is proved. These results are applied to Signorini problem with friction for which two error estimates and numerical examples are also given.
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References
Babuska, I., Azis, A.K.: The mathematical foundations of the finite-element methods with applications to partial differential equations. New York: Academic Press 1972
Bensoussan, A., Lions, J.L.: Nouvelle formulation de problèmes de contrôle impulsionnel et applications. C.R. Acad. Sc. Paris276, 1189–1192 (1973)
Brezis, H.: Equations et inéquations non linéaires dans les espaces vectoriels en dualité. Ann. Inst. Fourier.18, 115–175 (1968)
Ciarlet, P.G.: The finite element method for elliptic problems. Amsterdam: North-Holland 1978
Cocu, M.: Existence of solutions of Signorini problems with friction. Int. J. Engng. Sci.22, 567–575 (1984)
Duvaut, G.: Problèmes unilatéraux en mécanique des milieux continus. Actes, Congrès International des Mathématiciens, 71–77 (1970)
Duvaut, G.: Equilibre d'un solide élastique avec contact unilatéral et frottement de Coulomb. C.R. Acad. Sc. Paris290, 263–265 (1980)
Duvaut, G., Lions, J.L.: Les inéquations en mécanique et en physique. Paris: Dunod 1972
Glowinski, R.: Numerical methods for nonlinear variational problems. Berlin Heidelberg New York: Springer 1984
Glowinski, R., Lions, J.L., Tremolières, R.: Numerical analysis of variational inequalities. Amsterdam: North-Holland 1981
Haslinger, J., Tvrdy, M.: Approximation and numerical solution of contact problems with friction. Appl. Mat.28, 55–71 (1983)
Kikuchi, N., Song, Y.J.: Penalty/finite-element approximations of a class of unilateral problems in linear elasticity. Quart. Appl. Math.39, 1–22 (1981)
Oden, J.T., Pires, E.: Contact problems in elastostatics with non-local friction laws. TICOM Report, The University of Texas at Austin, pp. 81–12 (1981)