2019 Fiscal Year Final Research Report
Research on PDEs for fluids in terms of numerical and mathematical analysis
| Project/Area Number |
17K14230
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | The University of Tokyo |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Keywords | 有限要素法 / Navier-Stokes方程式 / 領域摂動 / Primitive方程式 / 最大正則性 / Stokes-Darcy問題 / 不連続Galerkin法 / Euler方程式 |
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| Outline of Final Research Achievements |
We studied partial differential equations describing the motion of fluids in terms of mathematical and numerical analysis. From the viewpoint of mathematics, we considered the primitive equations which are known as fundamental equations for atmosphere and ocean. We proved that there exists a good solution to the primitive equations and explained their relation with the Navier-Stokes equations, which are more fundamental in the context of fluid dynamics.
From the viewpoint of numerics, we considered the finite element method, which is one of the numerical methods to solve PDEs. We justified its use in domains with a smooth and curved boundary.
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| Free Research Field |
微分方程式の数値解析
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| Academic Significance and Societal Importance of the Research Achievements |
流体の数値シミュレーションにおいては、数値計算手法の急速な発展に比べて、数学的議論を用いた正当化が追いついていない面がある。本研究課題で得られた成果は、数学解析と数値解析の両面からアプローチを行い、欠落している数学的正当化を確立することを試みたものである。経験則で確認するという側面が強かった数値シミュレーションの妥当性を数学理論の面からもサポートし、流体数理の発展に寄与することが期待される。
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