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Study of numerical verification of Navier-Stokes equations

Research Project

Project/Area Number 14540141
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionMEIJI UNIVERSITY

Principal Investigator

KATSURADA Masashi  Meiji University, School of Science and Technology, Associate Professor, 理工学部, 助教授 (80224484)

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)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Keywordsnumerical verification / Stokes equation / Navier-Stokes equations / general outflow condition / 精度保障付き数値計算 / Navier Stokes方程式
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.

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (16 results)

All 2004 2002 Other

All Journal Article (11 results) Publications (5 results)

  • [Journal Article] A remark on the pressure for the Navier-Stokes flows in 2-D straight channel with an obstacle2004

    • Author(s)
      Morimoto, H.
    • Journal Title

      Mathematical Methods in the Applied Science 27

      Pages: 891-906

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A holomorphic semigroup approach to the lumped mass finite element method2004

    • Author(s)
      Saito, N.
    • Journal Title

      Journal of Computational and Applied Mathematics 169・1

      Pages: 71-85

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On the Stokes equation with the leak and slip boundary conditions of friction type : regularity of solutions2004

    • Author(s)
      Saito, N.
    • Journal Title

      Publications of RIMS, Kyoto University 40

      Pages: 345-383

    • NAID

      130003585558

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Remarks of the rational approximation of holotnorphic semigroups with notiuniform partitions2004

    • Author(s)
      Saito, N.
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 21・3

      Pages: 323-337

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A holomorphic semigroup approach to the lumped mass finite element method2004

    • Author(s)
      Saito, N.
    • Journal Title

      Journal of computational and Applied Math. 169-1

      Pages: 71-85

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On the Stokes equation with the leak and slip boundary conditions of friction type : regularity of solutions2004

    • Author(s)
      Saito, N.
    • Journal Title

      Publication of RIMS, Kyoto University 40

      Pages: 345-383

    • NAID

      130003585558

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Remarks of the rational approximation of holomorphic semigroups with nonuniform partitions2004

    • Author(s)
      Saito, N.
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 21-3

      Pages: 323-337

    • NAID

      10018379799

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A Remark on pressure for the Navier-Stokes flows in 2-D straight channel with an obstacle2004

    • Author(s)
      Morimoto, H.
    • Journal Title

      Mathematical Methods in the Applied Science 27

      Pages: 891-906

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Remarks on the rational approximation of holomorphic semigroups with nonuinform partitions2004

    • Author(s)
      Saito, N.
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 21・3

      Pages: 323-337

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A remark on the existence of steady Navier-Stokes flows in a certain two dimensional infinite tube2002

    • Author(s)
      Morimoto, H.(Fujita, H.と共著)
    • Journal Title

      Tokyo Journal of Mathematics 25・2

      Pages: 307-321

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A remark on the existence of steady-Navier-Stokes flows in a certain two dimensional infinite tube2002

    • Author(s)
      Morimoto, H.(with Fujita, H.)
    • Journal Title

      Tokyo Journal of Mathematics 25-2

      Pages: 307-321

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] 斉藤宣一, 鈴木貴(共著): "A finite difference scheme to the system of self-interacting particles"京都大学数理解析研究所考究録. 1320. 18-28 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 斉藤宣一: "A holomorphic semigroup approach to the lumped mass finite element method"Journal of Computational and Applied Mathematics. 169 No.1. 71-85 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 斉藤宣一: "On the Stokes equation with the leak and slip boundary conditions of friction type : regularity of solutions"Publication of RIMS, Kyoto University. 40. 345-383 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] 森本浩子, 藤田宏と共著: "A remark on the existence of steady Navier-Stokes flows in a certain two dimensional infinite tube"Tokyo Journal of Mathematics. Vol.25, No.2. 307-321 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 齊藤宣一, 鈴木貴と共著: "Numerical methods for nonlinear semigroups and degenerate parabolic euqations"京都大学数値解析研究所講究録. Vol.1254. 32-40 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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