Analysis and computation of a mean-field model for superconductivity
Superconductivity has been an outstanding field of extensive research in recent times. Several models for it exist now in the literature. In this paper, the authors study a mean-field model from analytical as well from computational points of view. Individual vortex-like structures are not resolved here, but the study includes effects due to pinning of vortices. The existence and uniqueness of solutions of a regularized version of the model are dealt with. Behaviour of the solutions as the regularization parameter vanishes is also investigated. Approximations based on semi-discrete and fully discrete finite-element-based discretizations are carefully formulated and analyzed in detail. A few computational experiments are carried out and numerical results thereof are neatly presented in eleven figures with discussion. The paper has a good analysis based on a variational inequality formulation and discrete approximations of a mean-field model for superconductivity. Future possibilities of generalization of the model and numerical analysis are pointed out. There are four theorems, three lemmas, two corollaries and thirteen references in the work.
scientific article; zbMATH DE number 1271903