Speaker: Prof. Yanping Chen (陈艳萍教授)

Time: 15:00-16:00, 18 May 2021 (Tuesday) (Beijing time)

Venue: T2-202

Abstract

We investigate a posteriori error analysis for hybridizable discontinuous Galerkin methods for convection diffusion equations. A residual-type error estimator without any postprocessing solutions is proposed, and we prove that the error estimator is robust with respect to the error measured by an easily calculated energy norm in the sense that the efficiency and reliability constants are independent of the diffusion coefficient. Then the result and the method, that have been obtained and used for convection diffusion equations, are applied to linear-quadratic distributed optimal control problems governed by convection diffusion equations. We use the variational discretization concept for the approximation of control, and an efficient and reliable error estimator is obtained for the error measured by an energy norm. Note that the estimator is also robust in the sense that the ratio of the upper and lower bounds is independent of the diffusion coefficient. Finally, several examples are provided to validate the performance of the obtained error estimators.

About Prof. Chen

陈艳萍，华南师范大学二级教授、博士生导师。2008 年被聘为广东省高等学校珠江学者特聘教授，2004 年享受国务院颁发的政府特殊津贴、入选教育部首批新世纪优秀人才支持计划，2002 年评为教育部首批全国高等学校优秀骨干教师。2017 年获教育部自然科学二等奖、2012 年获广东省科学技术二等奖、2011 年获湖南省自然科学一等奖、2008 年获教育部自然科学一等奖、2004 年获湖南省科学技术进步二等奖。出版专著《最优控制问题高效算法理论》（英文版，科学出版社，2015 年 11 月，由国家出版基金资助、入选信息与计算科学丛书）和教材《最优控制问题高效算法理论》（英文版）、《偏微分方程数值解》、《数值计算方法》和《数学建模教学与评估指南》，在 SIAM Numer. Anal.和Math. Comp.等国际一流学术期刊上发表了学术论文 264 篇，是 ESI 高被引论文作者，2014 年至 2020 年连续 7 年入选 Elsevier 中国高被引学者榜单。主持 1 项国家自然科学基金重点项目、7 项国家自然科学基金面上项目和 1 项国家自然科学基金重大研究计划培育项目等等。