Finite element analysis of a current density-electric field formulation of Bean's model for superconductivity

We study a current density-electric field formulation of Bean's model for the experimental set-up of an infinitely long cylindrical superconductor subject to a transverse magnetic field. We introduce a fully practical finite-element approximation of the model and prove an error between the exact solution and the approximate solution for the current density of order (h + Deltat)(1/2). Numerical simulations for a variety of given source currents are presented.