Analysis and computation of a mean-field model for superconductivity

A mean-held model for superconductivity is studied from both the analytical and computational points of view. In this model, the individual vortex-lik e 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. T he existence and uniqueness of solutions of a regularized version of the mo del are demonstrated and the behavior of these solutions as the regularizat ion parameter tends to zero is examined. Then, semi-discrete and fully disc rete finite element based discretizations are formulated and analyzed and t he results of some computational experiments are presented. Mathematics Sub ject Classification (1991): 65N30.