报告问题 (Title)：Energy stability of variable-step L1-type schemes for time-fractional Cahn-Hilliard model (时间分数阶Cahn-Hilliard模子变步长L1型名堂的能量稳固性)

报告人 (Speaker)：廖洪林 教授（南京航空航天大学）

报告时间 (Time)：2022年9月29日(周四) 14:00-15:30

报告所在 (Place)：线上腾讯聚会 （ID：453 779 895）

约请人(Inviter)：蔡敏

主理部分：理学院数学系

报告摘要：The positive definiteness of discrete time-fractional derivatives is fundamental to the numerical stability for time-fractional phase-field models. A novel technique is proposed to estimate the minimum eigenvalue of discrete convolution kernels generated by the nonuniform L1, half-grid based L1 and time-averaged L1 formulas of the fractional Caputo's derivative. The main discrete tools are the discrete orthogonal convolution kernels and discrete complementary convolution kernels. Certain variational energy dissipation laws at discrete levels of the variable-step L1-type methods are then established for time-fractional Cahn-Hilliard model. They are shown to be asymptotically compatible, in the fractional order limit $\alpha\rightarrow1$, with the associated energy dissipation law for the classical Cahn-Hilliard equation. Numerical examples together with an adaptive time-stepping procedure are provided to demonstrate the effectiveness of the proposed methods.