Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 3, p. 563-578

This contribution deals with a mixed variational formulation of 3D contact problems with the simplest model involving friction. This formulation is based on a dualization of the set of admissible displacements and the regularization of the non-differentiable term. Displacements are approximated by piecewise linear elements while the respective dual variables by piecewise constant functions on a dual partition of the contact zone. The rate of convergence is established provided that the solution is smooth enough. The numerical realization of such problems will be discussed and results of a model example will be shown.

DOI : https://doi.org/10.1051/m2an:2004026
Classification:  65N30,  74M15
Keywords: mixed finite element methods, unilateral contact problems with friction, a priori error estimates
@article{M2AN_2004__38_3_563_0,
     author = {Haslinger, Jaroslav and Sassi, Taoufik},
     title = {Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {3},
     year = {2004},
     pages = {563-578},
     doi = {10.1051/m2an:2004026},
     zbl = {1080.74046},
     mrnumber = {2075760},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2004__38_3_563_0}
}
Haslinger, Jaroslav; Sassi, Taoufik. Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 3, pp. 563-578. doi : 10.1051/m2an:2004026. http://www.numdam.org/item/M2AN_2004__38_3_563_0/

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