Verified eigenvalue estimation for elliptic differential operators and its application in non-linear problems
| Project/Area Number |
23740092
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Waseda University |
|---|
Principal Investigator |
LIU Xuefeng 早稲田大学, 理工学術院, 講師 (50571220)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
|---|
| 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 / 固有値の下界評価 / Lehmann-Goerisch の定理 / 非適合有限要素法 / 誤差評価 / 重調和微分作用素 / 微分作用素の固有値問題 / 高精度な誤差評価 / 非線形問題の解の検証 / 高精度な固有値評価 |
|---|
| 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.
|
Report
(4 results)
Research Products
(50 results)
