Space discretization for the Landau-Lifshitz-Gilbert equation with magnetostriction

We consider the conservation of momentum equation for the displacement vector together with a nonlinear dissipative magnetic law described by Landau-Lifshitz-Gilbert (LLG) equation. This system describes the magnetostriction caused by an applied magnetic field. We use a finite element approximation and we design a numerical scheme for computations. We derive the error estimates for the approximation of the displacement vector and the magnetization.