A finite element approximation of a variational formulation of Bean's model for superconductivity

We introduce a finite element approximation of a variational formulation of Bean's model for the physical configuration of an infinitely long cylindrical superconductor subject to a transverse magnetic field. We prove an error between the exact solution and the approximate solution for the current density and the magnetic field in appropriate norms of order h1/2 +\dt. Numerical simulations for a variety of applied magnetic fields are also presented.