Mixed finite element approximation of 3D contact problems with given friction: Error analysis and numerical realization
Department of Numerical Mathematics, Charles University
12116 Praha 2, Czech Republic. firstname.lastname@example.org.
2 Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR UFR Sciences Campus II, Bd Maréchal Juin, 14032 Caen Cedex, France. email@example.com.
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.
Mathematics Subject Classification: 65N30 / 74M15
Key words: Mixed finite element methods / unilateral contact problems with friction / a priori error estimates.
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