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.
Mots-clés : Diffusion equation, low-regularity solution, mixed formulation, eigenproblem, domain decomposition methods
@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://archive.numdam.org/articles/10.1051/m2an/2018011/}
}
TY - JOUR AU - Ciarlet, P. Jr. AU - Giret, L. AU - Jamelot, E. AU - Kpadonou, F.D. TI - Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 2003 EP - 2035 VL - 52 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2018011/ DO - 10.1051/m2an/2018011 LA - en ID - M2AN_2018__52_5_2003_0 ER -
%0 Journal Article %A Ciarlet, P. Jr. %A Giret, L. %A Jamelot, E. %A Kpadonou, F.D. %T Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 2003-2035 %V 52 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2018011/ %R 10.1051/m2an/2018011 %G en %F M2AN_2018__52_5_2003_0
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. http://archive.numdam.org/articles/10.1051/m2an/2018011/
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