报告题目：An efficient and unconditionally convergent Galerkin finite element method for the nonlinear Schrödinger equation: an alternative technique of convergence analysis
主讲人：王廷春教授（南京信息工程大学）
时间：2019年12月13日（周五）15:00
地点：北院卓远楼307会议室
主办单位：统计与数学学院
摘要：This talk aims to propose and analyze a linearized three-level Galerkin finite element method (FEM) for a generalized nonlinear Schrödinger equation. Differing from the popular Li-Sun's error-splitting technique where, as an intermediate step, construction and analysis of a corresponding time-discrete system is necessary, we here carry out an alternative analysis technique which is used to study directly the fully discrete numerical scheme and consequently establish the optimal L2 error estimate without any restriction on the grid ratio. Our analysis method can be extended to analyze error estimates of many traditional FEMs for some other partial differential equations. Several numerical results are reported to verify our theoretical analysis.
主讲人简介：
王廷春，现为南京信息工程大学数学与统计学院教授、博士生导师、计算数学团队负责人，江苏省“青蓝工程”中青年学术带头人，美国《数学评论》评论员，《Journal of Information and Computing Science》杂志副主编，江苏省计算数学学会常务理事。主要从事偏微分方程数值解和计算物理方面的研究工作，特别是在高维非线性Schrödinger型方程（组）的有限差分法、有限元法和谱方法的算法构造和算法分析方面做出一些研究成果。已在《Journal of Computational Physics》《Journal of Scientific Computing》《Advances in Computational Mathematics》《SCIENCE CHINA Mathematics》《Journal of Computational Mathematics》等主流期刊发表SCI检索论文40余篇，论文被引850余次。先后主持三项国家自然科学基金和一项江苏省自然科学基金面上项目。科研成果和教学成果分别获得江苏省高校自然科学奖一等奖和江苏省教学成果奖一等奖。
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