报告题目：The Positive Definiteness of the Integral-Averaged L1 (IAL1) Fractional Derivative Operator and its Application in H¹-norm Anlysis of the IAL1 Method

报 告 人：王元明, 华东师范大学 银河娱乐场 教授

报告时间：2025年6月3日（星期二）下午15：00

报告地点：7JC214

报告摘要：A new positive definiteness result for the integral-averaged L1 (IAL1) fractional-derivative operator is established. It improves the previous positive definiteness results in the literature and plays an important role in the analysis of H¹-norm error of the IAL1 method. Using this new positive definiteness result, we give an H¹-norm analysis of the stability and convergence of the IAL1 method for a time-fractional diffusion problem with a Caputo time-fractional derivative of order α∈(0,1) on nonuniform time meshes. The H¹-norm stability holds for the general nonuniform time meshes, while the H¹-norm convergence is proved for the time graded meshes and the H¹-norm convergence order in time is min{3 + α,γα}/2 for all α∈(0, 1), where γ ≥ 1 is the mesh grading parameter. Two full discretization methods using finite differences and finite elements in space are considered. The theoretical results are illustrated by numerical results. This is a joint work with Dr. Zi-Yun Zheng.

报告人简介：王元明，现为华东师范大学银河娱乐场 教授、博士生导师。1991年在西安交通大学获理学硕士学位，1996年在上海大学获理学博士学位，1996年6月至1998年6月在复旦大学从事博士后工作。学术研究方向为偏微分方程数值解，目前主要关注分数阶微分方程和积分-微分方程的数值方法, 在SIAM J Numer. Anal., Numer. Math. J Sci. Comput., Appl. Numer. Math., Numer. Algorithm等国内外专业期刊上发表学术研究论文九十余篇。