Error estimates for 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 equation. This system describes evolution of magnetization in deformable ferromagnets. We design a numerical scheme for full discretization and derive space–time a priori and a posteriori error estimates. The accuracy of the proposed method and efficiency of space–time adaptive algorithm based on the a posteriori estimates is illustrated numerically.