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    1. Energy stability of variable-step fractional BDF2 formula

      發布者:文明辦作者:發布時間:2022-11-23瀏覽次數:10


      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.

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