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Méthode d'éléments finis mixtes :application aux équations de la chaleur et de Stokes instationnaires

Abstract : This work intends to establish a priori error estimates for the approximate solutions of evolution equations obtained by the dual mixed method of finite elements in the spatial directions for three types of problems: the first one concerns the Cauchy problem for the heat diffusion equation; the second is the non-stationary Stokes problem and the last one concerns the Cauchy problem for the heat diffusion equation with a random diffusion coefficient. For these three types of problems, there is a certain number of reasons for prefering the dual mixed method in the spatial directions to a classical method in the spatial directions. Among these reasons, the fundamental property is the local conservation, thus a global one, of certain physical quantities (the quantity of movement, the mass, the quantity of heat can be mentioned). Another well-known reason for adopting the dual mixed method in the spatial directions is the fact that this method allows us to introduce new variables: p(t) =grad u(t) the heat flow at time t for the heat diffusion equation, p(t) = K ◊ u(t) the heat flux at time t for the heat diffusion equation with random diffusion coefficient K, or σ = grad u(t) the gradient tensor of the velocity field at time t for the non-stationary Stokes problem, these additional unknowns having a physical sense of particular importance for more than one application.
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https://tel.archives-ouvertes.fr/tel-00194195
Contributor : Réda Korikache <>
Submitted on : Wednesday, December 5, 2007 - 9:23:53 PM
Last modification on : Friday, March 26, 2021 - 1:58:51 PM
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Réda Korikache. Méthode d'éléments finis mixtes :application aux équations de la chaleur et de Stokes instationnaires. Mathématiques [math]. Université de Valenciennes et du Hainaut-Cambresis, 2007. Français. ⟨tel-00194195⟩

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