| Project/Area Number |
16540096
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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 | The University of Tokyo |
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Principal Investigator |
KIKUCHI Fumio University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院数理科学研究科, 教授 (40013734)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2006: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | numerical analysis / finite element method / a posteriori error estimate / hypercircle method / interpolation error constant / verification of accuracy / mixed and non-conforming methods / numerical experiment / 混合法 / 誤差定数 |
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| Research Abstract |
As a study of methods and techniques for a posteriori error estimation of the finite element method (FEM), we obtained the following results and observations.
1. Study of a posteriori error estimation based on the hypercircle method : For Poisson's equation, we have analyzed the above a posteriori method with the mixed FEM and related methods, and verified the results by numerical experiment. Some results were published in an international journal. The present method turns out to require very few error constants but its range of applicability is limited. We also search for its effectiveness in wider problems and non-conforming FEM.
2. Estimation of interpolation error constants : We analyzed various interpolation error constants appearing in the constant and conforming linear triangular finite elements. Quantitative evaluation of such constants is essential in a posteriori error estimation and Nakao's numerical verification method. The results were published in international journals. We also perform similar analysis for the non-conforming linear triangle.
3. Development and analysis of FEM for electromagnetics : Related to items 1 and 2, we have been studying FEM for electromagnetics. Some results for quadrilateral elements were published in an international journal as an international joint work. We are analyzing Maxwell's eigenvalue problems over axisymmetric domains by the Fourier FEM.
4. Study of plate bending FEM : We have studied and published a unification method for the Kirchhoff and Reissner-Mindlin elements in an international journal. We are now studying determination method for the transverse shear forces.
5. Study of the discontinuous Galerkin method : We start a posteriori error analysis of the discontinuous Galerkin method. The non-conforming FEM in item 2 is a classical example of such method, and is taken as a starting point of our study.
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