2013 Fiscal Year Final Research Report
Establishment of unified numerical methods for moving boundary problems
| Project/Area Number |
23540150
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Meiji University (2012-2013)
University of Miyazaki (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | 移動境界問題 / Hele-Shaw問題 / 曲率流方程式 / 曲率依存型接線速度 / 結晶成長 / スパイラル / 数値スキーム / 雪結晶 |
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| Research Abstract |
When the interface between different mediums moves, the interface is called moving boundary, and the problem of tracking moving boundaries mathematically and numerically is called moving boundary problem (MBP in short). In the present research, we have studied numerical methods for MBPs, and tried to develop quite general numerical schemes and establish unified numerical methods for various MBPs. Within the research periods, we could develop quite nice unified numerical methods for curvature flow equations which are typical MBPs. Mathematical proofs such as convergence of the numerical schemes are on-going research.
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