Energy stability of variable-step fractional BDF2 formula

主讲人：廖洪林 南京航空航天大学教授

时间：2022年11月29日9：30

地点：腾讯会议 220 106 816

举办单位：数理学院

主讲人介绍：廖洪林，应用数学博士，2018年至今任教于南京航空航天大学数学学院。2001年在解放军理工大学获理学硕士学位，2010年在东南大学获理学博士学位，2001-2017年任教于解放军理工大学。学术研究方向为偏微分积分方程数值解，目前主要关注相场以及多相流模型的时间变步长离散与自适应算法, 在Math Comp，SIAM J Numer Anal, SIAM J Sci Comput, IMA J Numer Anal, J Comput Phys, Sci China Math等国内外专业期刊上发表学术研究论文四十余篇。

内容介绍：A new discrete energy dissipation law of the variable-step fractional BDF2 (second-order backward differentiation formula) scheme is established for time-fractional Cahn-Hilliard model with the Caputo's derivative. We propose a novel discrete gradient structure by a local-nonlocal splitting technique, that is, the fractional BDF2 formula is split into a local part analogue to the two-step backward differentiation formula of the first derivative and a nonlocal part analogue to the L1-type formula of the Caputo's derivative. In the sense of the limit $\alpha\rightarrow1^-$, the discrete energy and the corresponding energy dissipation law are asymptotically compatible with the associated discrete energy and the energy dissipation law of the variable-step BDF2 method for the classical Cahn-Hilliard equation, respectively. Numerical examples with an adaptive stepping procedure are provided to demonstrate the accuracy and the effectiveness of our proposed method.