Optimal Error Estimates of Linearized Crank–Nicolson Galerkin Method for Landau–Lifshitz Equation

This paper focuses on the optimal error estimates of a linearized Crank–Nicolson scheme for the Landau–Lifshitz (LL) equation describing the evolution of spin fields in continuum ferromagnets. We present a rigorous analysis for the regularity of the local strong solution to LL equation with Neumann boundary conditions. The proof of the optimal error estimates are based upon an error splitting technique proposed by Li and Sun. Numerical results are provided to confirm our theoretical analysis.