报告题目：A Finite Element Elasticity Complex in Three Dimensions

主 讲 人：黄学海

单 位：上海财经大学

时 间：12月9日9:00

腾 讯 ID：352 894 727

摘 要：

A finite element elasticity complex on tetrahedral meshes is devised. The H^1 conforming finite element is the smooth finite element developed by Neilan for the velocity field in a discrete Stokes complex. The symmetric div-conforming finite element is the Hu-Zhang element for stress tensors. The construction of an H(inc)-conforming finite element for symmetric tensors is the main focus of this paper. The key tools of the construction are the decomposition of polynomial tensor spaces and the characterization of the trace of the inc operator. The polynomial elasticity complex and Koszul elasticity complex are created to derive the decomposition of polynomial tensor spaces. The trace of the inc operator is induced from a Green's identity. Trace complexes and bubble complexes are also derived to facilitate the construction. Our construction appears to be the first H(inc)-conforming finite elements on tetrahedral meshes without further splits.

简 介：

黄学海，上海财经大学教授、博士研究生导师，研究方向为偏微分方程数值解，致力于高阶偏微分方程、弹性力学问题的高效数值方法以及离散张量微分复形方面的研究工作。在Math. Comp.、SIAM J. Numer. Anal.、Numer. Math.、J. Sci. Comput.等国际期刊发表学术论文30余篇。主持国家自然科学基金面上项目2项，主持上海市自然科学基金原创探索项目1项，主持完成国家自然科学基金青年项目、数学天元项目和温州市科技计划项目各1项、浙江省自然科学基金项目2项，参与多项国家自然科学基金面上项目和浙江省自然科学基金项目。获中国计算数学学会优秀青年论文竞赛优秀奖，博士学位论文被评为上海市研究生优秀成果(学位论文)。