华中科技大学李东方教授学术报告

报告题目：Unconditionally Optimal Error Analysis of Crank–Nicolson Galerkin FEMs for a Strongly Nonlinear Parabolic System

报告人：李东方 教授

主持人：安荣  教授

报告时间： 2020年11月23日下午15：30——16：30

腾讯会议：ID 898-267-303

摘 要：In this talk, we present unconditionally optimal error estimates of linearized Crank-Nicolson Galerkin finite element methods for a strongly nonlinear parabolic system in R^d (d=2,3). However, all previous works required certain time-step conditions that were dependent on the spatial mesh size. In order to overcome several difficulties caused by the strong nonlinearity of the system, the proof takes two steps. First, by using a temporal-spatial error splitting argument and a new technique, optimal $L^2$ error estimates of the numerical schemes can be obtained under the condition $\tau\geq h$, where $\tau$ denotes the time-step size and $h$ is the spatial mesh size. Second, we obtain the boundedness of numerical solutions by mathematical induction and inverse inequality when $\tau\leq h$. Then, optimal $L^2$ and $H^1$ error estimates are proved in a different way for such case. Numerical results are given to illustrate our theoretical analysis.

 李东方教授简介

李东方，华中科技大学数学与统计学院教授，博导，中国系统仿真学会仿真算法专业委员会委员。曾先后赴加拿大McGill大学，香港城市大学从事博士后研究。主要研究微分方程数值解、系统仿真和信号处理等领域，在微分方程保结构算法和分数阶微分方程的高效数值算法和理论上取得一些有意义的进展。主要工作发表在《SIAM. J. Numer. Anal.》，《SIAM. J. Sci. Comput.》、《J. Comp. Phys.》、《Appl. Comp. Harm. Appl.》、《J. Sci. Comput》等多个国际著名计算学科SCI期刊上，多篇为高被引论文。