2023 Fiscal Year Final Research Report
Finite element methods for nonlinear partial differential equations on curved domains
| Project/Area Number |
19K14590
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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| Keywords | 有限要素法 / 偏微分方程式 / 数値解法 / 誤差評価 / 不連続Galerkin時間離散化法 |
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| Outline of Final Research Achievements |
I investigated the finite element method for partial differential equations with smooth boundaries and related topics from various viewpoints. In particular, I obtained many important resultsfor elliptic and parabolic partial differential equations, such as the maximum norm estimates and the discontinuous Galerkin time-stepping method. In addition, I studied numerical methods for solving time-evolving curves and I applied them to mathematical analysis of a minimizing problem for curves.
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| Free Research Field |
数値解析学
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| Academic Significance and Societal Importance of the Research Achievements |
有限要素法はその柔軟性や数学的な明快さから, シミュレーション分野で広く用いられている数値解法である. 有限要素法に対する数学的な解析は, シミュレーションの妥当性を数学的に保証するために重要な研究である. 本研究成果は特に, 現実問題のシミュレーションの問題設定として現れうる問題を考えているため, シミュレーション分野において重要な役割を果たしている.
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