Geodesic
Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 5, pp. 2003-2035

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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.

DOI : 10.1051/m2an/2018011
Classification : 65N25, 65N30, 82D75
Keywords: Diffusion equation, low-regularity solution, mixed formulation, eigenproblem, domain decomposition methods

Ciarlet, P. Jr. 1 ; Giret, L. 1 ; Jamelot, E. 1 ; Kpadonou, F.D. 1

1 
@article{M2AN_2018__52_5_2003_0,
     author = {Ciarlet, P. Jr. and Giret, L. and Jamelot, E. and Kpadonou, F.D.},
     title = {Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2003--2035},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {5},
     year = {2018},
     doi = {10.1051/m2an/2018011},
     zbl = {1460.65137},
     mrnumber = {3891752},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018011/}
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Ciarlet, P. Jr.; Giret, L.; Jamelot, E.; Kpadonou, F.D. Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 5, pp. 2003-2035. doi: 10.1051/m2an/2018011

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