报告题目：Divdiv Conforming Finite Element for Symmetric Tensors

报 告 人：陈龙 教授 University of California at Irvine

报告时间：2020年7月28日 11:00

报告地点：Zoom ID：941 567 2172

密码：2020135

校内联系人：王翔 wxjldx@jlu.edu.cn

报告摘要：

Two types of finite element spaces on triangles and tetrahedrons are constructed for div-div conforming symmetric tensors in two and three dimensions. Besides the normal-normal component, another trace involving combination of first order derivatives of stress should be continuous across the sides of the element. Due to the rigid of polynomials, the stress tensor element is also continuous at vertices, and on the plane orthogonal to each edge in three dimensions. Hilbert complex and polynomial complexes are presented and several decomposition of polynomial vector and tensors spaces are revealed from the complexes. The constructed div-div conforming elements are exploited to discretize the mixed formulation of the biharmonic equation. Optimal order and superconvergence error analysis is provided. The standard Lagrange element basis can be used to implement the hybridized formulation.

This is a joint work with Xuehai Huang from Shanghai University of Finance and Economic.

报告人简介：

陈龙现为加州大学尔湾分校教授。1997年本科毕业于南京大学，此后硕士毕业于北京大学，博士毕业于美国宾夕法尼亚州立大学，博士论文获宾夕法尼亚州立大学的Alumin奖。先后在美国加州大学圣地亚哥分校、马里兰大学从事博士后研究工作，2007年起在加州大学尔湾分校工作至今 。主要研究兴趣为偏微分方程的数值方法、自适应有限元方法的理论和应用、多重网格方法的设计和分析、网格生成和计算几何。陈龙教授在这些方面做出非常杰出的工作，在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comput. 等计算数学顶级期刊上发表论文40余篇，参编著作多部。是Computers and Mathematics with Applications，Multiscale Modeling and Simulation 等SCI期刊的编委，主持美国自然科学基金项目3项、美国能源部项目1项。