2009 Fiscal Year Final Research Report
Study of finite element analysis on differential manifolds
| Project/Area Number |
19540135
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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 |
TSUCHIYA Takuya Ehime University, 大学院・理工学研究科, 教授 (00163832)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Takashi 大阪大学, 大学院・基礎工学研究科, 教授 (40114516)
OHTSUKA Hiroshi 愛媛大学, 大学院・理工学研究科, 准教授 (30203839)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 数値解析学 / 楕円型境界値問題 / 自由境界問題 / Hadamard変分 |
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| Research Abstract |
Suppose that we are interested in an elliptic boundary value problem defined on a bounded domain. In this research, we consider effects of perturbation of the domain to the solution of the boundary value problem. In particular, we have established a scheme of computing the first and second variations of functionals defined with the solution of BVP. Using the scheme, we have found an alternative proof of the classical Hadamard's variational formula. We also apply the scheme to the research of a free boundary problem called the "dam problem". We have obtained the first and second variation of the functional which governs the dam problem. Using the obtained the first variation, we propose a new iterative algorithm for numerical solution of the dam problem.
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