It is proposed a finite-element method to analyse critical-state problems for type-II superconductivity numerically. The authors are particularly interested in the situation where a bulk superconductor is located in a 3D domain.
In the first part of the present paper the authors recall the mathematical models of the eddy current problem and the critical-state constitutive laws and formulate the models as evolution variational inequalities. After formulating the discretization of the variational inequality formulations, the authors establish the convergence of the sequence of approximations to the anlytical solutions. In the final of the paper the abstract results are implemented numerically. The authors discuss the behaviour of the magnetic field and the distribution of the current density flowing through a bulk cubic superconductor in an uniform magnetic field.