2013 Fiscal Year Final Research Report
A basic study for establishment of practical structure-preserving finite element method
| Project/Area Number |
23560063
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Engineering fundamentals
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| Research Institution | The University of Tokyo |
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Principal Investigator |
MATSUO Takayasu 東京大学, 情報理工学(系)研究科, 教授 (90293670)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 数値解析 / 偏微分方程式 |
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| Research Abstract |
The aim of the present study is to improve the "discrete partial derivative method" which has been devised in the preceding project of the author by combining finite element method and the concept of structure-preserving methods so that it becomes more practical in actual computations.
In this project, first the author introduced the concept of L2 projection, and by utilizing the concept, proposed a new framework in which we can construct structure-preserving finite element schemes automatically, Due to this, any users can now construct structure-preserving finite element schemes by simply following the procedure, and thus the practicality of the method has been highly improved. Second, we proposed a new principle for a structure-preserving method that bases on discontinuous Galerkin method. This can drastically decrease the computational cost and improve the flexibility of the schemes.
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