Full discretization scheme for linearized quasi-static Maxwell's equations with a non-linear boundary condition

We study a time dependent eddy current equation for the magnetic field H accompanied with a non-linear degenerate boundary condition, which is a generalization of the classical Silver-Muller condition for a non-perfect conductor. More exactly, the relation between the normal components of electric-E and magnetic-H fields obeys the following power law v x E = v x (vertical bar H x v vertical bar(alpha-1) H x v) for some alpha epsilon (0, 1]. We design a linear fully discrete approximation scheme to solve this nonlinear degenerate problem. The convergence of the approximations to a weak solation is proved, error estimates describing the dependance of the error on discretization parameters are derived as well