Energy stability of variable-step fractional BDF2 formula


主讲人:廖洪林 南京航空航天大学教授


地点:Tencent会议 220 106 816


主讲人先容: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。

内容先容: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.

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