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Généralisation de la méthode Nitsche XFEM pour la discrétisation de problèmes d'interface elliptiques

Nelly Barrau 1, 2
2 CONCHA - Complex Flow Simulation Codes based on High-order and Adaptive methods
Inria Bordeaux - Sud-Ouest, UPPA - Université de Pau et des Pays de l'Adour, CNRS - Centre National de la Recherche Scientifique : UMR5142
Abstract : This thesis focuses on the generalization of the NXFEM method proposed by A. and P. Hansbo for elliptic interface problem. Numerical modeling and simulation of flow in fractured media are at the heart of many applications, such as petroleum and porous media (reservoir modeling, presence of faults, signal propagation, identification of layers ...), aerospace (problems of shock, rupture), civil engineering (concrete cracking), but also in cell biology (deformation of red blood cells). In addition, many research projects require the development of robust methods for the consideration of singularities, which is one of the motivations and objectives of the Concha team and of this thesis. First a modification of this method was proposed to obtain a robust method not only with respect to the mesh-interface geometry, but also with respect to the diffusion parameters. We then looked to its generalization to any type of 2D-3D meshes (triangles, quadrilaterals, tetrahedra, hexahedra), and for any type of finites elements (conforming, nonconforming, Galerkin discontinuous) for plane and curved interfaces. The applications have been referred to the flow problems in fractured porous media : adaptation of NXFEM method to solve an asymptotic model of faults, to unsteady problems, transport problems, or to multi-fractured domains.
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https://tel.archives-ouvertes.fr/tel-00913387
Contributor : Nelly Barrau <>
Submitted on : Tuesday, December 3, 2013 - 3:54:32 PM
Last modification on : Friday, January 15, 2021 - 9:21:16 AM
Long-term archiving on: : Monday, March 3, 2014 - 11:20:44 PM

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  • HAL Id : tel-00913387, version 1

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Nelly Barrau. Généralisation de la méthode Nitsche XFEM pour la discrétisation de problèmes d'interface elliptiques. Analyse numérique [math.NA]. Université de Pau et des Pays de l'Adour, 2013. Français. ⟨NNT : 2013PAUU3025⟩. ⟨tel-00913387⟩

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