2013 Fiscal Year Final Research Report
Verified eigenvalue estimation for elliptic differential operators and its application in non-linear problems
| Project/Area Number |
23740092
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Waseda University |
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Principal Investigator |
LIU Xuefeng 早稲田大学, 理工学術院, 講師 (50571220)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 固有値評価 / 有限要素法 / 事前誤差評価 / 非線形偏微分方程式 / 精度保証付き数値計算 / 楕円型微分作用素 / 固有値問題 / Hypercircle equation |
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| Research Abstract |
The eigenvalue problem for differential operators is a basic problem in both engineering and mathematics. The upper bounds for the Laplacian have been given in history, but the lower bounds remain to be very difficult. In this research, a new algorithm is developed to give lower bounds for the eigenvalues of the Laplacian. Such an algorithm is based on the finite element method along with the use of the hypercircle equation. It is the first method that can easily deal with eigenvalue problems on domain of general shapes. The eigenvalue bounds are also successfully applied to solution verification for nonlinear partial differential equations defined on arbitrary polygonal domains.
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Research Products
(27 results)
