| Issue |
ESAIM: M2AN
Volume 59, Number 6, November-December 2025
|
|
|---|---|---|
| Page(s) | 3341 - 3362 | |
| DOI | https://doi.org/10.1051/m2an/2025090 | |
| Published online | 17 December 2025 | |
Optimal L2 convergence of renormalized Crank–Nicolson mass lumping fems for the Landau–Lifshitz equation
1
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
2
Beijing Computational Science Research Center, Beijing 100193, P.R. China
3
School of Science, Harbin Institute of Technology, Shenzhen 518055, P.R. China
4
School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, P.R. China
* Corresponding author: wangjilu@hit.edu.cn, wangjilu03@gmail.com
Received:
5
July
2024
Accepted:
15
October
2025
The paper is concerned with a linearly semi-implicit renormalized Crank–Nicolson mass lumping finite element method (FEM) for solving the Landau–Lifshitz equation, which models the dynamics of magnetization under a non-convex constraint of unit magnetization length. The numerical solutions preserve the unit length at all finite element nodes by means of renormalizations. Based on a new superconvergence result and a new geometric relation between the errors of the auxiliary solution and the renormalized numerical solution, we rigorously establish optimal L2 error estimates of the proposed scheme. Numerical experiments are presented to illustrate the temporal and spatial convergence of the algorithm.
Mathematics Subject Classification: 65M12 / 65M60 / 35K61
Key words: Landau–Lifshitz equation / finite element methods / Crank–Nicolson method / renormalizations / optimal error estimates
© The authors. Published by EDP Sciences, SMAI 2025
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