An adaptive high order finite element method for arbitrarily shaped domains with automatic mesh generation

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:陈志明(中国科学院)
:2024-11-18 16:30
:海韵园行政楼C503

报告人:陈志明中国科学院

 间:2024111816:30

 点:海韵园行政楼C503

内容摘要:

We consider high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems, which release the work of body-fitted mesh generation and allow us to design adaptive finite element methods for solving curved geometric singularities. We introduce new concepts of the large element and interface deviation to solve the small cut cell problem of unfitted finite element methods. We consider the reliable implementation of the adaptive method, which extends our previous work on the reliable cell merging algorithm for smooth interfaces to automatically generate the induced mesh for piecewise smooth interfaces. An $hp$ a posteriori error estimate is derived for a new unfitted finite element method whose finite element functions are conforming in each subdomain. Numerical examples illustrate the competitive performance of the method. This talk is based on joint works with Ke Li, Yong Liu and Xueshuang Xiang. 

人简介

陈志明,中国科学院院士,中国科学院数学与系统科学研究院研究员、博士生导师。1986年陈志明毕业于南京大学数学系;1989年获得中国科学院数学研究所硕士学位;1992年从德国奥格斯堡大学博士毕业后在德国慕尼黑工业大学从事博士后研究工作;1994年回国后进入中国科学院数学研究所工作,历任助理研究员、副研究员、研究员;1999年担任中国科学院数学与系统科学研究院研究员;2000年获得国家杰出青年科学基金资助;2006年应邀在国际数学家大会上做邀请报告;20171128日当选为中国科学院院士。

 

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