@article{Gu2026, 
author = {Haonan Gu and Shusen Xie},
title = {Error Estimates of Projection Finite Element Method for Landau-Lifshitz Equation},
year = {2026},
journal = {Periodical of Ocean University of China},
volume = {56},
number = {11},
pages = {152-162},
keywords = {Landau-Lifshitz equation, Crank-Nicolson scheme, sphere projection method, finite element method, error estimates},
url = {https://www.sciopen.com/article/10.16441/j.cnki.hdxb.20250160},
doi = {10.16441/j.cnki.hdxb.20250160},
abstract = {This paper establishes a Crank-Nicolson projection finite element scheme for the Landau-Lifshitz equation, and derives unconditional optimal error estimates. By employing the temporal-spatial error splitting technique, the error between the exact solution and the numerical solution is decomposed into three components: the temporal error, the spatial error and the spherical projection error. First, the temporal error is analyzed by introducing a linearized time-discrete system, and the regularity of the solution for this time-discrete system is rigorously proved. Second, based on the time-discrete system, a spatial error equation independent of the time step τ is derived. Under the condition that the time step and spatial step are unrestricted, the optimal error estimate of the projection finite element method in the L2 norm is demonstrated. Moreover, numerical experiments on model problems are conducted to validate the theoretical results and the effectiveness of the proposed method.}
}