Displaying similar documents to “Convergence results of the fictitious domain method for a mixed formulation of the wave equation with a Neumann boundary condition”

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

Jaroslav Haslinger, Taoufik Sassi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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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...

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...

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,...

A mixed–FEM and BEM coupling for a three-dimensional eddy current problem

Salim Meddahi, Virginia Selgas (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.