2003 Fiscal Year Final Research Report Summary
Mathematical Theory of Error Analysis of Finite Element Methods
| Project/Area Number |
14540122
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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-U, Dept.Math.Sci, Professor, 理学部, 教授 (00163832)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAGUTI Sigeru Ehime-U, Dept.Math.Sci, Professor, 理学部, 教授 (50215620)
FANG Qing Ehime-U, Dept.Math.Sci, Instructor, 理学部, 助手 (10243544)
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| Project Period (FY) |
2002 – 2003
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| Keywords | finite elements / error analysis / Galerkin methods / Mathematical foundation |
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| Research Abstract |
In this research project, we have tried to develop a mathematical theory of error analysis of finite element methods, and have obtained the following results.
(1)We have consider on error analysis of Galerkin methods applied to (non-) linear equations with a (linear or nonlinear) compact term defined in Hilbert space setting. We have found a simple way of developing mathematical theory of error analysis of Galerkin methods applied to such equations.
(2)We have proved rigorously the convergence of trial free boundary methods applied to the Dam Problem, which is a typical elliptic free boundary problem.
(3)We have consider on error analysis of the piecewise quadratic finite element method applied to 2-point boundary value problems defined on 1-dimensional bounded interval. We have found that all known error bounds are still valid even if coefficient function of the principle term is not-continuous or entirely positive.
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