A robust linearization scheme for nonlinear diffusion in type-II superconductors

We study a nonlinear partial differential equation strongly motivated by the modelling of processes in type-II superconductors in a bounded domain along with appropriate boundary condition. We design a robust and efficient linear approximation scheme based on fix-point principle. The convergence of approximations to a weak solution of the original problem is proved. We also present some numerical examples to show the efficiency of the proposed method.