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Schémas boîte : étude théorique et numérique

Abstract : The main objet of this thesis is the theoretical and numerical analysis of box schemes. In the case of elliptic problems, the basic principle is to average the two continuous equations given by the mixed form of the problem, onto the boxes of the mesh. Box schemes belong to the category of so-called mixed Petrov-Galerkin finite volume methods. Firstly, I studied the 2D mixed form of the Poisson problem with a box scheme on triangular or quadrangular meshes. As part of the research group MoMaS for deep ground repositories of radioactive wastes, the potential interest of box schemes for unstationary convection-diffusion problems has been tested. A box scheme has been designed for the 1D equation. Two kinds of upwinding are introduced, each one being designed to cure the two classical oscillations sources present in the approximation of convective-diffusion equations. The generalization to the 2D case is perfomed using an ADI-like method.
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Isabelle Greff. Schémas boîte : étude théorique et numérique. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2003. Français. ⟨NNT : 2003METZ025S⟩. ⟨tel-01749815⟩



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