報告題目：Divdiv Conforming Finite Element for Symmetric Tensors
報 告 人：陳龍 教授 University of California at Irvine
報告時間：2020年7月28日 11:00
報告地點：Zoom ID：941 567 2172
密碼：2020135
校内聯系人：王翔 wxjldx@jlu.edu.cn
報告摘要：
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.
報告人簡介：
陳龍現為加州大學爾灣分校教授。1997年本科畢業于南京大學，此後碩士畢業于北京大學，博士畢業于美國賓夕法尼亞州立大學，博士論文獲賓夕法尼亞州立大學的Alumin獎。先後在美國加州大學聖地亞哥分校、馬裡蘭大學從事博士後研究工作，2007年起在加州大學爾灣分校工作至今 。主要研究興趣為偏微分方程的數值方法、自适應有限元方法的理論和應用、多重網格方法的設計和分析、網格生成和計算幾何。陳龍教授在這些方面做出非常傑出的工作，在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comput. 等計算數學頂級期刊上發表論文40餘篇，參編著作多部。是Computers and Mathematics with Applications，Multiscale Modeling and Simulation 等SCI期刊的編委，主持美國自然科學基金項目3項、美國能源部項目1項。
