NUMERICAL ANALYSIS OF THE MIXED FINITE ELEMENT METHOD FOR THE NEUTRON DIFFUSION EIGENPROBLEM WITH HETEROGENEOUS COEFFICIENTS

被引:4
|
作者
Ciarlet Jr, P. [1 ]
Giret, L. [1 ,2 ]
Jamelot, E. [3 ]
Kpadonou, F. D. [1 ,4 ]
机构
[1] ENSTA ParisTech, POEMS, CNRS, INRIA, 828 Bd Marechaux, F-91762 Palaiseau, France
[2] Univ Paris Saclay, LLPR, CEA, DEN,SERMA, F-91191 Gif Sur Yvette, France
[3] Univ Paris Saclay, LMSF, CEA, DEN,STMF, F-91191 Gif Sur Yvette, France
[4] UVSQ, Lab Math Versailles, 45 Av Etats Unis, F-78035 Versailles, France
来源
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2018年 / 52卷 / 05期
关键词
Diffusion equation; low-regularity solution; mixed formulation; eigenproblem; domain decomposition methods; DOMAIN DECOMPOSITION METHODS; APPROXIMATION; REGULARITY; MEDIA;
D O I
10.1051/m2an/2018011
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
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页码:2003 / 2035
页数:33
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