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.
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: Mod\'elisation math\'ematique et analyse num\'erique}, pages = {563--578}, publisher = {EDP-Sciences}, volume = {38}, number = {3}, year = {2004}, doi = {10.1051/m2an:2004026}, mrnumber = {2075760}, zbl = {1080.74046}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an:2004026/} }
TY - JOUR AU - Haslinger, Jaroslav AU - Sassi, Taoufik TI - Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 563 EP - 578 VL - 38 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004026/ DO - 10.1051/m2an:2004026 LA - en ID - M2AN_2004__38_3_563_0 ER -
%0 Journal Article %A Haslinger, Jaroslav %A Sassi, Taoufik %T Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 563-578 %V 38 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004026/ %R 10.1051/m2an:2004026 %G en %F 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: Modélisation mathématique et analyse numérique, Volume 38 (2004) no. 3, pp. 563-578. doi : 10.1051/m2an:2004026. http://www.numdam.org/articles/10.1051/m2an:2004026/
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