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New Development of Conforming Finite Elements -- Beyond Nedelec

发布者:大发dafa888      发布时间:2020-07-01      浏览次数:68

报告人:张智民 教授

报告时间:2020年72上午9:00

报告方式:腾讯会议  会议ID:778 812 043

报告人及内容简介:

张智民,美国韦恩州立大学教授、Charles H. Gershenson 杰出学者,世界华人数学家大会两次45分钟报告人,现任和曾任10个国内外数学杂志编委,包括Mathematics of Computation、Journal of Scientific Computing、Numerical methods for Partial Differential Equations 、Journal of Mathematical Study、Journal of Computational Mathematics、CSIAM Transaction on Applied Mathematics、《数学文化》等。发表SCI论文180余篇,论文google引用4600余次,主持过10个美国国家基金会的项目。

张智民教授1982年在中国科学技术大学数学系毕业取得学士学位,1985年在中国科学技术大学数学系毕业取得硕士学位,师从石钟慈院士,1991年在美国马里兰大学取得博士学位,师从有限元专家美国工程院院士Ivo Babuska教授。

张智民教授长期从事计算方法,尤其是有限元方法的研究,在超收敛、后验误差估计、自适应算法和PDE特征值计算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年被大型商业软件COMSOL Multiphysics 采用。

In two ground breaking papers (1980 and 1986), Nedelec proposed $H(curl)$-conforming elements to solve electromagnetic equations that contains the “curl” operator. It is more or less as the $H^1$-conforming elements (or $C^0$ elements) for elliptic equations that contains the “grad” 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. Recently, there have been some research in solving electromagnetic equations which involve four “curl” operators. Hence, construction of $H(curlcurl)$-conforming elements becomes necessary. In this work, we construct$H(curl curl)$-conforming elements for rectangular and triangular meshes and apply them to solve quad-curl equations as well as related eigenvalue problems. 

 


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