Abdellatif Agouzal

Estimations d'erreurs en lois de comportement

Resume On presente un estimateur derreur a posteriori pour le probleme de diffusion qui evalue lerreur en loi de comportement : ∥▽ ũ h - p h ∥ 0,Ω , ou ũ h est une ≪ approximation ≫ conforme de la variable primale et p h est une approximation conforme de ▽ u obtenue par un post-traitement de lapproximation P 1 non conforme de u . Cette methode est etendue au probleme de Stokes. Des resultats similaires peuvent etre demontres pour le probleme de lelasticite lineaire.

A posteriori error estimates in finite element methods for general Friedrichs' systems

Abstract In this paper we develop and analyse a new a posteriori error estimator for general Friedrichs systems valid for most classical finite element approximations. This error estimator is based on comparison between an appropriate norm of the exact error, and the L 2 -norm of the residuals of the approximate solution. We prove that the estimator is independent of the dimension of the space and of the numerical approximation method used. Moreover the global majoration and local minoration constants are independent of the shape of the mesh.

Equilibrium method to approximate elliptic problems with non-standard boundary conditions

A non-standard Equilibrium Method to solve some elliptic problems with non-standard boundary conditions is presented. A conforming primal variational formulation is used on the boundary, whereas an equilibrium one is established on the domain. One hereby obtains a coupled system, in which all matching conditions remain implicit. Existence and uniqueness results of the approximate solution are given, and the convergence rate of the method is specified for a model problem.

On a posteriori error estimator for primal, equilibrium and mixed approximation of diffusion equations

In this paper, we present an a posteriori error estimator for diffusion equation with the solution obtained by Black-box solver. The estimator is valid for classical primal, equilibrium and mixed finite element approximations with or without numerical integration.

Approximation d'un problème de l'élasticité non linéaire par une méthode d'éléments finis mixtes

Resume Dans cette Note on introduit une nouvelle formulation mixte a trois champs approchant les deplacements, le gradient des deplacements et les contraintes du probleme de lelasticite non lineaire. Le probleme obtenu est non lineaire et sera approche par les espaces de type Raviart–Thomas. Nous montrons lexistence et lunicite de la solution du probleme approche et etablissons des estimations a priori derreur optimales.