2004 Fiscal Year Final Research Report Summary
Study of numerical verification of Navier-Stokes equations
| Project/Area Number |
14540141
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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 | MEIJI UNIVERSITY |
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Principal Investigator |
KATSURADA Masashi Meiji University, School of Science and Technology, Associate Professor, 理工学部, 助教授 (80224484)
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| Co-Investigator(Kenkyū-buntansha) |
MORIMOTO Hiroko Meiji University, School of Science and Technology, Professor, 理工学部, 教授 (50061974)
SAITO Norikazu Toyama University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00334706)
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| Project Period (FY) |
2002 – 2004
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| Keywords | numerical verification / Stokes equation / Navier-Stokes equations / general outflow condition |
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| Research Abstract |
According to studies by Mitsuhiro Nakao, Nobito Yamamoto and Yoshitaka Watanabe (1995-1999), Katsurada developed numerical verification programs solving Dirichlet problems of steady Stokes equation and steady Navier-Stokes equation in a two-dimensional rectangular domain. Those programs were originally written in C++ language using a C++ class library "Profil/BIAS" supporting interval operations. Later they were rewritten by using MATLAB Toolbox "INTLAB" so that they are considerably readable and effective. (Indeed we also tried developing a MATLAB-like interpreter that can handle interval operations, whereas it could not compete with MATLAB+INTLAB.) We adopted those programs to reconfirm the results by Nakao group, and found the followings : (1)(constructive a priori estimate) our results coincide with theirs up to 14-15 digits, (2)(a posteriori estimate) our results coincide with theirs up to 3-5 digits (they only presented numerical results with 5 digits).
Hiroko Morimoto has been studied Navier-Stokes flows under general outflow condition. In particular, she proved existence of solution in a certain two dimensional infinite tube.
Norikazu Saito studied several problems concerning finite element method such as (1)regularity of weak solution to Stokes equation with leak and slip boundary condition of friction type, (2)holomorphic semigroup approach to the lumped mass finite approximation.
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