题目：Asymptotically compatible energy dissipation laws of variable-step L1-type schemes for time-fractional Cahn-Hilliard model

报告人：廖洪林教授 南京航空航天大学

时间：2022年5月30日下午14:00-16:00

腾讯会议：304-425-557    会议密码：0530

邀请人：汪志波

主持人：乔守红

摘要：We address the positive definiteness of discrete time-fractional derivatives, which is fundamental to the numerical stability (in the energy sense) for time-fractional phase-field models. A novel technique is proposed to estimate the minimum eigenvalue of discrete convolution kernels generated by the nonuniform L1, half-grid based L1 and time-averaged L1 formulas of the fractional Caputo's derivative. The main discrete tools are the discrete orthogonal convolution kernels and discrete complementary convolution kernels. Certain variational energy dissipation laws at discrete levels of the variable-step L1-type methods are then established for time-fractional Cahn-Hilliard model. They are shown to be asymptotically compatible, in the fractional order limit alpha rightarrow 1, with the associated energy dissipation law for the classical Cahn-Hilliard equation. Numerical examples together with an adaptive time-stepping procedure are provided to demonstrate the effectiveness of the proposed methods.

专家简介：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，正主持国家自然科学基金面上项目1项，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三十余篇。