In this article, the energy stability of two high-order L2 schemes for time-fractional phase-field equations is established. We propose a reformulation of the L2 operator and also some new properties on it. We prove the energy boundedness (by initial energy) of an L2 scalar auxiliary variable scheme for any phase-field equation and the fractional energy law of an implicit-explicit L2 Adams--Bashforth scheme for the Allen--Cahn equation. The stability analysis is based on a new Cholesky decomposition proposed recently by some of us.

翻译：在本篇文章中,确定了两个高阶L2计划对时间折射阶段-实地方程式的能源稳定性。我们建议重订L2操作员和其中的一些新特性。我们证明了任何阶段-实地方程式的L2卡路里辅助变量计划的能源约束(最初能源),以及Allen-Cahn等式的隐含L2 Adams-Bashforth计划的分数能源法。稳定分析基于我们有些人最近提出的新的Cholesky分解法。