Error bounds for the FEM numerical solution of non-linear field problems

A bound for a norm of the difference between the computed and exact solution vectors for static, stationary or quasistationary non-linear magnetic fields is derived by employing the polarization fixed point iterative method. At each iteration step, the linearized field is computed by using the finite element method. The error introduced in the iterative procedure is controlled by the number of iterations, while the error due to the chosen discretization mesh is evaluated on the basis of the hypercircle principle.