Study on finite element exterior calculus
| Project/Area Number |
22540139
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ehime University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TAKASHI Suzuki 大阪大学, 基礎工学研究科, 教授 (40114516)
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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 |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 1次補間 / 有限要素法 / 外接半径条件 / １次補間 / 三角形要素 / 領域の摂動 / Riemann多様体 / ラプラシアン / 自由境界問題 / リーマン多様体 / Hadamard変分 |
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| Research Abstract |
We have found “the circumradius condition” for linear interpolation on triangular elements. We proved it without using validated numerical computation. We then found that the circumradius condition is closely related to the definition of surface area. That is, we proved that if a surface has a certain regularity and inscribed surfaces satisfy the circumradius condition, the area of inscribed surfaces converges to that of the surface. Since the theorem can be applied to “Schwarz’s lantern”, the theorem is “best-possible” with respect to geometry of triangulation.
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Report
(4 results)
Research Products
(34 results)
