Analysis and computation of a mean-field model for superconductivity

Abstract.

A mean-field model for superconductivity is studied from both the analytical and computational points of view. In this model, the individual vortex-like structures occuring in practical superconductors are not resolved. Rather, these structures are homogenized and a vortex density is solved for. The particular model studied includes effects due to the pinning of vortices. The existence and uniqueness of solutions of a regularized version of the model are demonstrated and the behavior of these solutions as the regularization parameter tends to zero is examined. Then, semi-discrete and fully discrete finite element based discretizations are formulated and analyzed and the results of some computational experiments are presented.