A quasi-variational inequalar problem in superconductivar

We derive a class of analytical solutions and a dual formulation of a scalar two-space-dimensional quasi-variational inequal-AR problem in applied superconductiv-AR. We approximate this formulation by a fully practical finite element method based on the lowest order RaviartThomas element, which yields approximations to both the primal and dual variables (the magnetic and electric fields). We prove the subsequence convergence of this approximation, and hence prove the existence of a solution to both the dual and primal formulations, for strictly star-shaped domains. The effectiveness of the approximation is illustrated by numerical examples with and without this domain restriction.