A three-field augmented Lagrangian formulation  of unilateral
 contact problems with cohesive forces

David Doyen; Alexandre Ern; Serge Piperno

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Displaying similar documents to “A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces”

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ESAIM: Mathematical Modelling and Numerical Analysis

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We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential,...

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A unilateral contact 2D-problem is considered provided one of two elastic bodies can shift in a given direction as a rigid body. Using Lagrange multipliers for both normal and tangential constraints on the contact interface, we introduce a saddle point problem and prove its unique solvability. We discretize the problem by a standard finite element method and prove a convergence of approximations. We propose a numerical realization on the basis of an auxiliary “bolted” problem and the...

Mixed finite element approximation of 3D contact problems with given friction : error analysis and numerical realization

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ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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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...

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F. Brezzi (1978)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Mixed formulation of elliptic variational inequalities and its approximation

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The approximation of a mixed formulation of elliptic variational inequalities is studied. Mixed formulation is defined as the problem of finding a saddle-point of a properly chosen Lagrangian $2$ on a certain convex set $K x Λ$ . Sufficient conditions, guaranteeing the convergence of approximate solutions are studied. Abstract results are applied to concrete examples.