Voir la notice de l'article provenant de la source Numdam
In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterizes the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current to the magnetic flux, and the parallel component of the current to the magnetic flux in bulk type-II superconductor. The existence of a solution to the variational inequality formulation is proved and the representation theorem of subdifferential for a class of energy functionals including our energy is established. The variational inequality formulation is discretized in time by a semi-implicit scheme and in space by the edge finite element of lowest order on a tetrahedral mesh. The fully discrete formulation is an unconstrained optimisation problem. The subsequence convergence property of the fully discrete solution is proved. Some numerical results computed under a rotating applied magnetic field are presented.
@article{M2AN_2008__42_3_333_0,
author = {Kashima, Yohei},
title = {On the double critical-state model for {type-II} superconductivity in {3D}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {333--374},
publisher = {EDP-Sciences},
volume = {42},
number = {3},
year = {2008},
doi = {10.1051/m2an:2008010},
mrnumber = {2423790},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008010/}
}
TY - JOUR AU - Kashima, Yohei TI - On the double critical-state model for type-II superconductivity in 3D JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2008 SP - 333 EP - 374 VL - 42 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008010/ DO - 10.1051/m2an:2008010 LA - en ID - M2AN_2008__42_3_333_0 ER -
%0 Journal Article %A Kashima, Yohei %T On the double critical-state model for type-II superconductivity in 3D %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2008 %P 333-374 %V 42 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008010/ %R 10.1051/m2an:2008010 %G en %F M2AN_2008__42_3_333_0
Kashima, Yohei. On the double critical-state model for type-II superconductivity in 3D. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 3, pp. 333-374. doi: 10.1051/m2an:2008010
Cité par Sources :