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

¹ POEMS, ENSTA ParisTech, CNRS, INRIA, 828 Bd des Maréchaux, 91762 Palaiseau Cedex, France.
² DEN-Service d’Etudes des Réacteurs et de Mathématiques Appliquées-SERMA, LLPR, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France.
³ DEN-Service de Thermo-hydraulique et de Mécanique des Fluides-STMF, LMSF, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette Cedex, France.
⁴ Laboratoire de Mathématiques de Versailles, UVSQ, 45 Av des Etats-Unis, 78035 Versailles Cedex, France.

^* Corresponding author: erell.jamelot@cea.fr

Received: 7 July 2017
Accepted: 25 January 2018

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.