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...

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...

In this paper, the convergence of a
Neumann-Dirichlet algorithm to approximate Coulomb's contact
problem between two elastic bodies is proved in a continuous setting. In this algorithm, the natural interface between the two bodies is retained as a decomposition zone.

We study the Stokes problems in a bounded planar domain $\Omega $ with a friction type boundary condition that switches between a slip and no-slip stage. Our main goal is to determine under which conditions concerning the smoothness of $\Omega $ solutions to the Stokes system with the slip boundary conditions depend continuously on variations of $\Omega $. Having this result at our disposal, we easily prove the existence of a solution to optimal shape design problems for a large class of cost functionals. In order to release...

In this paper, we present and study a mixed variational method in order to approximate, with the finite element method, a Stokes problem with Tresca friction boundary conditions. These non-linear boundary conditions arise in the modeling of mold filling process by polymer melt, which can slip on a solid wall. The mixed formulation is based on a dualization of the non-differentiable term which define the slip conditions. Existence and uniqueness of both continuous and discrete solutions of these...

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