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

TL;DR

This paper presents a new spatial discretization method using Localized Orthogonal Decomposition for simulating magnetization dynamics governed by the Landau-Lifshitz equation, with detailed error analysis and validation.

Contribution

It introduces a novel LOD-based spatial discretization for the LL equation, providing systematic error estimates and demonstrating improved accuracy.

Findings

Validated the accuracy of the proposed scheme through numerical examples

Decomposed the total error into temporal and spatial components

Established optimal error estimates for the discretization

Abstract

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.