2012 Fiscal Year Final Research Report
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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| 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 |
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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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