| Project/Area Number |
26400201
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Ehime University |
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Principal Investigator |
Tsuchiya Takuya 愛媛大学, 理工学研究科(理学系), 教授 (00163832)
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| Co-Investigator(Kenkyū-buntansha) |
小林 健太 一橋大学, 大学院商学研究科, 准教授 (60432902)
鈴木 貴 大阪大学, 基礎工学研究科, 教授 (40114516)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 誤差解析 / 関数補間 / 有限要素法 / 外接半径 / Lagrage補間 / （射影）外接半径 / Crouzeix-Raviart補間 / 曲面の面積 / Lagrange補間 / 差分商 / 外接半径条件 / 最小・最大角条件 |
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| Outline of Final Research Achievements |
In this study, we have considered the error analysis of Lagrange interpolation on triangles and tetrahedrons (hereafter, we call them "elements"). Usually, the error analysis of Lagrange interpolation is done under the condition that elements are not so degenerate (or not so “flat”). We have found that essential factor of the error estimation is the (projected) circumradius of elements, and presented new error estimations expressed in terms of the (projected) circumradius and the diameter of elements.
According to the newly obtained error estimation, we can say that if the (projected) circumradius of elements converges to 0, the error of Lagrange interpolations also converges to 0, even if elements are become very flat. Therefore, if we use triangulations with such elements, finite element methods would provide reliable numerical solutions.
We believe that the newly obtained error estimation provide a new insights to finite element methods and numerical simulations.
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