论文标题
Lévy-Fokker-Planck方程的渐近保存方案的均匀误差估计值
Uniform error estimate of an asymptotic preserving scheme for the Lévy-Fokker-Planck equation
论文作者
论文摘要
我们为lévy-fokker-planck（LFP）方程中提出的渐近保存方案建立了均匀的缩放误差估计。主要困难不仅源于缩放参数和数值参数之间的相互作用，还源于平衡状态尾巴的缓慢衰减。我们通过根据缩放$ε$的相对大小分开参数域来解决这些问题：在$ε$很大的政权中，我们设计了一个加权规范来减轻脂肪尾巴引起的问题，而在$ε$的情况下，在$ε$很小的情况下，我们证明了LFP对其分数扩散限制的强大逆转率，并具有expicit insexit insexit insemit insemit insemit insement insexity inselfence。该方法将传统的AP估计扩展到无法统一界限的情况。我们的结果适用于任何维度和整个分数功率的跨度。
We establish a uniform-in-scaling error estimate for the asymptotic preserving scheme proposed in \cite{XW21} for the Lévy-Fokker-Planck (LFP) equation. The main difficulties stem from not only the interplay between the scaling and numerical parameters but also the slow decay of the tail of the equilibrium state. We tackle these problems by separating the parameter domain according to the relative size of the scaling $ε$: in the regime where $ε$ is large, we design a weighted norm to mitigate the issue caused by the fat tail, while in the regime where $ε$ is small, we prove a strong convergence of LFP towards its fractional diffusion limit with an explicit convergence rate. This method extends the traditional AP estimates to cases where uniform bounds are unavailable. Our result applies to any dimension and to the whole span of the fractional power.
