Landau-Lifshitz-Gilbert方程二阶BDF方法的后验误差分析
A posteriori error analysis for the second-order BDF method for the Landau-Lifshitz-Gilbert equation
AI总结：
针对LLG方程的切平面格式，基于二阶BDF方法与任意阶有限元推导后验误差估计，为其全自适应算法提供数学基础。
AI中文摘要：
切平面格式（TPS）是Landau-Lifshitz-Gilbert（LLG）方程已确立的离散格式，但尚未建立严格的后验误差估计。本研究基于时间方向的二阶向后微分公式（BDF(2)）和空间方向任意多项式次数的有限元，推导了TPS的严格后验误差估计。所提估计量为变时间步长自适应网格上的时间与空间离散误差提供了可计算的上界，该结果为LLG方程的全自适应算法奠定了数学基础。
英文摘要：
The tangent plane scheme (TPS) is a well-established discretization of the Landau-Lifshitz-Gilbert (LLG) equation. However, rigorous a posteriori error estimates have not been established. In this work, we derive a rigorous a posteriori error estimate for the TPS based on the second-order backward differentiation formula (BDF(2)) in time and finite elements of arbitrary polynomial degree in space. The proposed estimators provide computable upper bounds for the temporal and spatial discretization errors on adaptive meshes with variable time-step sizes. This result establishes the mathematical foundation for fully adaptive algorithms for the LLG equation.
