Energy stability of variable-step fractional BDF2 formula

主講人：廖洪林 南京航空航天大學教授

時間：2022年11月29日9：30

地點：騰訊會議 220 106 816

舉辦單位：數理學院

主講人介紹：廖洪林，應用數學博士，2018年至今任教于南京航空航天大學數學學院。2001年在解放軍理工大學獲理學碩士學位，2010年在東南大學獲理學博士學位，2001-2017年任教于解放軍理工大學。學術研究方向為偏微分積分方程數值解，目前主要關注相場以及多相流模型的時間變步長離散與自適應算法, 在Math Comp，SIAM J Numer Anal, SIAM J Sci Comput, IMA J Numer Anal, J Comput Phys, Sci China Math等國內外專業期刊上發表學術研究論文四十余篇。

內容介紹：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.