報(bào)告題目：An efficient and unconditionally convergent Galerkin finite element method for the nonlinear Schr?dinger equation: an alternative technique of convergence analysis
主講人：王廷春教授（南京信息工程大學(xué)）
時(shí)間：2019年12月13日（周五）15:00
地點(diǎn)：北院卓遠(yuǎn)樓307會(huì)議室
主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)院
摘要：This talk aims to propose and analyze a linearized three-level Galerkin finite element method (FEM) for a generalized nonlinear Schr?dinger 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.
主講人簡介：
王廷春，現(xiàn)為南京信息工程大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授、博士生導(dǎo)師、計(jì)算數(shù)學(xué)團(tuán)隊(duì)負(fù)責(zé)人，江蘇省“青藍(lán)工程”中青年學(xué)術(shù)帶頭人，美國《數(shù)學(xué)評(píng)論》評(píng)論員，《Journal of Information and Computing Science》雜志副主編，江蘇省計(jì)算數(shù)學(xué)學(xué)會(huì)常務(wù)理事。主要從事偏微分方程數(shù)值解和計(jì)算物理方面的研究工作，特別是在高維非線性Schr?dinger型方程（組）的有限差分法、有限元法和譜方法的算法構(gòu)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》等主流期刊發(fā)表SCI檢索論文40余篇，論文被引850余次。先后主持三項(xiàng)國家自然科學(xué)基金和一項(xiàng)江蘇省自然科學(xué)基金面上項(xiàng)目。科研成果和教學(xué)成果分別獲得江蘇省高校自然科學(xué)獎(jiǎng)一等獎(jiǎng)和江蘇省教學(xué)成果獎(jiǎng)一等獎(jiǎng)。
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