Displaying similar documents to “Mixed finite element approximation of 3D contact problems with given friction: Error analysis and numerical realization ”

Locking-Free Finite Elements for Unilateral Crack Problems in Elasticity

Z. Belhachmi, J.-M. Sac-Epée, S. Tahir (2009)

Mathematical Modelling of Natural Phenomena

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We consider mixed and hybrid variational formulations to the linearized elasticity system in domains with cracks. Inequality type conditions are prescribed at the crack faces which results in unilateral contact problems. The variational formulations are extended to the whole domain including the cracks which yields, for each problem, a smooth domain formulation. Mixed finite element methods such as PEERS or BDM methods are designed to avoid locking for nearly incompressible materials...

Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition

Eliane Bécache, Jeronimo Rodríguez, Chrysoula Tsogka (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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The problem of modeling acoustic waves scattered by an object with Neumann boundary condition is considered. The boundary condition is taken into account by means of the fictitious domain method, yielding a first order in time mixed variational formulation for the problem. The resulting system is discretized with two families of mixed finite elements that are compatible with mass lumping. We present numerical results illustrating that the Neumann boundary condition on the object is...

Mixed formulations for a class of variational inequalities

Leila Slimane, Abderrahmane Bendali, Patrick Laborde (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A general setting is proposed for the mixed finite element approximations of elliptic differential problems involving a unilateral boundary condition. The treatment covers the Signorini problem as well as the unilateral contact problem with or without friction. Existence, uniqueness for both the continuous and the discrete problem as well as error estimates are established in a general framework. As an application, the approximation of the Signorini problem by the lowest order mixed...

The treatment of “pinching locking” in -shell elements

Dominique Chapelle, Anca Ferent, Patrick Le Tallec (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a family of shell finite elements with quadratic displacements across the thickness. These elements are very attractive, but compared to standard general shell elements they face another source of numerical locking in addition to shear and membrane locking. This additional locking phenomenon – that we call “pinching locking” – is the subject of this paper and we analyse a numerical strategy designed to overcome this difficulty. Using a model problem in which only this specific...

error estimates for linear exterior problems mixed-FEM and DtN mappings

Mauricio A. Barrientos, Gabriel N. Gatica, Matthias Maischak (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we combine the dual-mixed finite element method with a Dirichlet-to-Neumann mapping (given in terms of a boundary integral operator) to solve linear exterior transmission problems in the plane. As a model we consider a second order elliptic equation in divergence form coupled with the Laplace equation in the exterior unbounded region. We show that the resulting mixed variational formulation and an associated discrete scheme using Raviart-Thomas spaces are well posed,...

An upwinding mixed finite element method for a mean field model of superconducting vortices

Zhiming Chen, Qiang Du (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we construct a combined upwinding and mixed finite element method for the numerical solution of a two-dimensional mean field model of superconducting vortices. An advantage of our method is that it works for any unstructured regular triangulation. A simple convergence analysis is given without resorting to the discrete maximum principle. Numerical examples are also presented.