Researches on the high-accurate computation and numerical verification for the solution of the partial differential equation with singularity
| Project/Area Number |
22740059
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hitotsubashi University (2011-2012)
Kanazawa University (2010) |
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Principal Investigator |
KOBAYASHI Kenta 一橋大学, 大学院・商学研究科, 准教授 (60432902)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 精度保証付き数値計算 / 誤差評価 / 偏微分方程式 / 特異性 / 補間誤差 / 有限要素法 / 三角形要素 / 四面体要素 / 補間誤差評価 / 非線形方程式 / 補間誤差定数 / 流体方程式 / 解の存在と一意性 / 爆発解 / 精度保証 / 非凸領域 / メッシュリファインメント / 無限次元固有値問題 |
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| Research Abstract |
The estimate for the interpolation error plays an essential role in error estimation for Finite Element Method. In our research, we obtained and proved precise formula that bounds interpolation error on the triangular elements. In particular, we proved that the interpolation error is bounded by the radius of circumscribed circle of the triangles. We call this condition circum radius condition. This result enables us to compute solutions of partial differential equation with singularity by efficient mesh division.
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Report
(4 results)
Research Products
(20 results)
