Homogenization of the Landau-Lifshitz equation

2020/12/23 by Lena Leitenmaier, Leitenmaier, Lena, Olof Runborg +1
Computer Science · Engineering · #35B27 #65M15 #82D40 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2012.12567

openalex publication_date 2020/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider homogenization of the Landau-Lifshitz equation with a highly oscillatory material coefficient with period ε modeling a ferromagnetic composite. We derive equations for the homogenized solution to the problem and the corresponding correctors and obtain estimates for the difference between the exact and homogenized solution as well as corrected approximations to the solution. Convergence rates in ε over times O(ε^σ) with 0≤ σ≤ 2 are given in the Sobolev norm H^q, where q is limited by the regularity of the solution to the detailed Landau-Lifshitz equation and the homogenized equation. The rates depend on q, σ and the the number of correctors.

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