题目：Anisotropic Error Estimates of Virtual Element Methods

时间：2018年8月28日10:00-11:00

地点：数学楼202讨论室

主办单位：数学学院

个人简介：陈龙，美国加州大学欧文分校教授，北京科学与工程研究院教授，北京市“海聚工程”入选专家。1997年在南京大学获得学士学位，2000年在北京大学获得硕士学位，2005年在Pennsylvania State University获得博士学位。主要研究兴趣有偏微分方程数值分析、自适应有限元理论、多重网格算法设计与分析和网格生成与优化。主持美国自然科学基金项目三项，发表科研论文50余篇，任SCI杂志编委。

摘要：A refined a priori error analysis of the conforming and non-conforming Virtual Element Method (VEM) is developed for approximating a model Poisson problem. A set of new geometric assumptions is proposed on shape regularity of polygonal meshes. A new universal error equation for the VEM is derived for any choice of stabilization, and a new stabilization using broken half-seminorm is introduced to incorporate short edges naturally into the a priori error analysis on isotropic elements. The error analysis is then extended to a special class of anisotropic elements with high aspect ratio originating from a body-fitted mesh generator, which uses? straight lines to cut a shape regular background mesh. Lastly, some commonly used tools for triangular elements are revisited for polygonal elements to give an in-depth view of these estimates' dependence on shapes.