Fix-point linearization schemes for nonlinear steady-state eddy current problems

We study a nonlinear degenerate partial differential equation strongly motivated by the modelling of processes in type-II superconductors in a bounded domain along with appropriate boundary conditions. We design a robust and efficient linear approximation scheme based on fix-point principle. We prove the convergence of approximations to a weak solution of the original problem. Some numerical experiments are presented in order to illustrate the efficiency of the proposed method.