A convergent finite element approximation for the quasi-static Maxwell–Landau–Lifshitz–Gilbert equations

We propose a θθ-linear scheme for the numerical solution of the quasi-static Maxwell–Landau–Lifshitz–Gilbert (MLLG) equations. Despite the strong nonlinearity of the Landau–Lifshitz–Gilbert equation, the proposed method results in a linear system at each time step. We prove that as the time and space steps tend to zero (with no further conditions when θ∈(12,1]), the finite element solutions converge weakly to a weak solution of the MLLG equations. Numerical results are presented to show the applicability of the method.