Optimal Error Estimates of a Linearized Backward Euler Localized Orthogonal Decomposition for the Landau-Lifshitz Equation

We introduce a novel spatial discretization technique for the reliable and efficient simulation of magnetization dynamics governed by the Landau-Lifshitz (LL) equation. The overall discretization error is systematically decomposed into temporal and spatial components. The spatial error analysis is conducted by formulating the LL equation within the framework of the Localized Orthogonal Decomposition (LOD) method. Numerical examples are presented to validate the accuracy and approximation properties of the proposed scheme.