学 术 报 告

报告题目：H(curl curl)-conforming and H(grad curl)-conforming finite elements---beyond Nedelec

报告人： 张智民 教授 （北京计算科学研究中心）

报告时间：2020年10月22日上午11:00-12:00

地点： 理学院五楼数学研究中心多媒体报告厅

44118太阳成城集团

2020.10.22

报告摘要: In his two ground breaking papers(1980 and 1986), Nedelec proposed H(curl)-        conforming and H(div)-conforming elements to solve second-order electromagnetic equations    that contains the “curl” and “div” operators. It is more or less as the $H^1$-conforming elements (or $C^0$ elements) for second-order elliptic equations that contains the $(grad)^2$ operator. As is well known in the finite element method literature, in order to solve 4th-order elliptic        equations such as the bi-harmonic equation, $H^2$-conforming elements (or $C^1$-elements) were developed. Recent years, there have been some research in solving electromagnetic equa-  tions which involve $curl^4$ operator and $(curl grad)^2$ operator. Hence, construction of H  (curl curl)-conforming and H(grad curl)-conforming elements becomes necessary. In this work, we report some recent development in this direction.

报告人简介:张智民，美国韦恩州立大学教授、博士生导师，Charles H. Gershenson 杰出学者，“长江学者奖励计划”讲座教授，世界华人数学家大会45分钟报告人。曾任美国数学学会杂志“Mathematics of Computation”、Springer杂志“Journal of Scientific Computing”的编委，现任Numerical methods for Partial Differential Equations 、Journal of Mathematical Study、Journal of Computational Mathematics、International Journal of Numerical analysis & Modeling、Discrete and Continuous dynamical Systems -- Series B 等多个国际计算和应用数学杂志以Mathematical Culture(《数学文化》)的编委。
长期从事计算方法，尤其是有限元方法的研究，在超收敛、后验误差估计和自适应算法等领域的开拓性研究取得了多项创新成果。在国际上第一个建立起广为流行的ZZ离散重构格式的数学理论，并首次提出了基于多项式守恒的离散重构格式。所提出的多项式保持重构（Polynomial Preserving Recovery—PPR）方法2008年被国际上广为流行的大型商业软件 COMSOL Multiphysics 采用。在国际计算数学主流杂志发表学术论文140余篇，得到国内外同行的广泛关注和引用。