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Méthodes d'éléments finis et estimations d'erreur a posteriori

Abstract : In this thesis, we develop a posteriori error estimators, for the finite element approximation of the time-harmonic Maxwell and reaction-diffusion equations. Introducing first, for Maxwell's system, residual type estimators, we study the dependence of the constants appearing in the lower and upper bounds with respect to the variation of the coefficients of the equation we consider. Then, we construct another type of estimator, based on equilibrated fluxes and the resolution of local problems, that we study for the reaction-diffusion equations and Maxwell's system. With all the estimators built for the Maxwell equation, we propose a comparison through numerical tests involving particular solutions on uniform meshes and refinement procedures with adaptive meshes. Finally, we propose an extension, for diffusion equations, of the equilibrated estimators to the discontinuous Galerkin finite element methods.
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Contributor : Sarah Dhondt-Cochez <>
Submitted on : Monday, January 28, 2008 - 11:39:24 AM
Last modification on : Friday, November 13, 2020 - 8:44:12 AM
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  • HAL Id : tel-00220484, version 1



Sarah Dhondt-Cochez. Méthodes d'éléments finis et estimations d'erreur a posteriori. Mathématiques [math]. Université de Valenciennes et du Hainaut-Cambresis, 2007. Français. ⟨tel-00220484⟩



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