What is ``good" shape of elements in FEM

2016 Fiscal Year Final Research Report

• Project/Area Number: 15K13454
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: The University of Tokyo
• Principal Investigator: Saito Norikazu 東京大学, 大学院数理科学研究科, 教授 (00334706)
• Co-Investigator(Renkei-kenkyūsha): SUITO Hiroshi 岡山大学, 環境生命科学研究科, 教授 (10302530) ; YAMADA Takahiro 横浜国立大学, 環境情報研究院, 教授 (40240022) ; TSUCHIYA Takuya 愛媛大学, 理工学研究科, 教授 (00163832)
• Research Collaborator: KOBAYASHI Kenta 一橋大学, 商学研究科, 准教授 (60432902) ; OIKAWA Issei 早稲田大学, 理工学術院, 研究員 (10637466)
• Project Period (FY): 2015-04-01 – 2017-03-31
• Keywords: 有限要素法 / 要素分割 / 誤差評価 / 不連続ガレルキン法

Outline of Final Research Achievements

The finite element method is a fundamental technology and its validity is guaranteed by the mathematical theory. In particular, regarding the shape of elements and the mathematical properties of finite element solutions, various things are known besides convergence and stability. However, even with the simplest triangle primary element, there is no consistent theory expressing mathematically and clearly what is the good element shape or what is a good triangulation. In this research, using various finite elements, we studied the following: (1) error of nodal interpolation (2) Condition number of coefficient matrix and nonuniformity of triangulation (3) Analytical properties such as discrete maximum principle and maximal regularity.

Free Research Field

数値解析