| 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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| 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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