主講人：廖洪林 南京航空航天大學(xué)教授

時(shí)間：2022年11月29日9：30

地點(diǎn)：騰訊會(huì)議 220 106 816

舉辦單位：數(shù)理學(xué)院

主講人介紹：廖洪林，應(yīng)用數(shù)學(xué)博士，2018年至今任教于南京航空航天大學(xué)數(shù)學(xué)學(xué)院。2001年在解放軍理工大學(xué)獲理學(xué)碩士學(xué)位，2010年在東南大學(xué)獲理學(xué)博士學(xué)位，2001-2017年任教于解放軍理工大學(xué)。學(xué)術(shù)研究方向?yàn)槠⒎址e分方程數(shù)值解，目前主要關(guān)注相場(chǎng)以及多相流模型的時(shí)間變步長(zhǎng)離散與自適應(yīng)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(guó)內(nèi)外專(zhuān)業(yè)期刊上發(fā)表學(xué)術(shù)研究論文四十余篇。

內(nèi)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.