Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients

Patrick Ciarlet 1 Léandre Giret 2, 1 Erell Jamelot 3 Félix Kpadonou 4, 5
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
2 LLPR - Laboratoire de Logiciels pour la Physique des Réacteurs
DM2S - Département de Modélisation des Systèmes et Structures : DEN/DM2S/SERMA/LLPR
Abstract : We study first the convergence of the finite element approximation of the mixed diffusion equations with a source term, in the case where the solution is of low regularity. Such a situation commonly arises in the presence of three or more intersecting material components with different characteristics. Then we focus on the approximation of the associated eigenvalue problem. We prove spectral correctness for this problem in the mixed setting. These studies are carried out without, and then with a domain decomposition method. The domain decomposition method can be non-matching in the sense that the traces of the finite element spaces may not fit at the interface between subdomains. Finally, numerical experiments illustrate the accuracy of the method.
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Patrick Ciarlet, Léandre Giret, Erell Jamelot, Félix Kpadonou. Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients. 2017. ⟨hal-01566179v2⟩

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