Research on the efficient calculation and numerical verification for the 3-d finite element method

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400198
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Hitotsubashi University
• Principal Investigator: KOBAYASHI Kenta 一橋大学, 大学院商学研究科, 准教授 (60432902)
• Co-Investigator(Kenkyū-buntansha): TSUCHIYA Takuya 愛媛大学, 大学院理工学研究科, 教授 (00163832)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 有限要素法 / 補間誤差評価 / Lagrange補間 / 四面体要素 / 精度保証付き数値計算

Outline of Final Research Achievements

In our research, we focused on the error analysis of the 3-dimensional finite element method and its application to the numerical verification method. The analysis of the interpolation error is particularly important for the error analysis of the finite element methods. In the preceding researches, the error analysis of the interpolation is done under the geometric assumptions such as the shape regularity or the generalized maximum angle condition. On the other hand, we present a new type of error estimation for the Lagrange interpolation which requires no geometric condition on tetrahedrons. This result would be applied to the numerical verification for the partial differential equation in the 3-dimensional problems based on the finite element method.

Free Research Field

数値解析