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1998 Fiscal Year Final Research Report Summary

Study of Domain Decomposition and Domain Interface Problems.

Research Project

Project/Area Number 09640297
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

FUJITA Hiroshi  Meiji Univ.Dept.of Math.Professor, 理工学部, 教授 (80011427)

Co-Investigator(Kenkyū-buntansha) KAWARADA Hideo  Chiba Univ.Dept.of Appl.Math Professor, 工学部, 教授 (90010793)
KATSURADA Masashi  Meiji Univ.Dept.of Math.Lecturer, 理工学部, 講師 (80224484)
FURUHASHI Rohzo  Meiji Univ.Dept.of Math.Professor, 理工学部, 教授 (40061973)
KONNO Reiji  Meiji Univ.Dept.of Math.Professor, 理工学部, 教授 (20061921)
MORIMOTO Hiroko  Meiji Univ.Dept.of Math.Professor, 理工学部, 教授 (50061974)
Project Period (FY) 1997 – 1998
KeywordsStokes Equation / Variatinal Inequality / Uzawa Algorithm / Domain Decomposition Method / inf-sup Condition / General Outflow Condition / Navier-Stokes Equation / Boundary Condition of Friction Type
Research Abstract

The main results of our study are as follows.
1. Boundary Conditions of Frictional Type
The basic mathematical problem for stationary Stokes flow under the boundary condition for friction type has been solved by the kead investigator when he gave a series of lectures at College de France in 1993, by use of the theory of Variation Inequalities. As a result of the present study, a certain saddle-point search formulation of the problem has been developed, which regards the pressure as a kind of Lagrange multiplier. As a consequence, we have obtained a better convergence theory for the Uzawa algorithms applied to these nonlinear problems.
2. Mathematical Study of DDM
In 1994, the head investigator proposed a new method to analyze the convergence speed of iterations arising from the domain decomposition method for elliptic equations , which yields a kind of optimal rates of convergence under certain geometrical assumtions on the relationship among sub-domains. Through the present study, a young collaborator, Norikazu Saito has succeeded to strengthen this method, which is sometimes called Fujita's method, so that the Stokes equation can be dealt with nicely. Saito makes use of some crucial estimates based on the so-called inf-supcondition for sub-domains.
3.Solvability of the Navier-Stokes Equation under General Outflow Condition
The head investigator has succeeded in proving, by means of a constructive a priori estimate, the solvability of the 2-dimensional and "symmetric "boundary value problems for the stationary Navier-Stokes flows under the general outflow (flux) condition. The crucial step of the proof might be called the method of virtual drains. Some nontrivial generalizations have been made by the head investigator and another investigator Hiroko Morimoto.

  • Research Products

    (39 results)

All Other

All Publications (39 results)

  • [Publications] H. Fujita: "A remark on the existence of the Navier-Stokes flow with non-vanishing outflow condition" Gakuto Intern.Series, Math.Sci. Appl.10. 53-61 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 藤田宏: "領域分割法の収束に関する解析的ならびに数値的研究, I," 明治大学技研紀要. 35-8. 103-135 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujita: "Stability analysis of Navier-Stokes flows in annuli" Math.Meth.Appl.Sci.20. 959-978 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kawarada: "Navier-Stokes flows coupled with potential flow through porous media" DDM in Sciences and Engineering, John Wiley. 8. 403-410 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujita: "An analytical study of optimal speed of convergence of iterations in DDM under certain shape assumptions of domains" Computational Sciences for 21st Century, John Wiley. 139-148 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujita: "On stationary solutions to Navier-Stokes equation in symmetric plane domains under general outflow condition" Pitman Research Notes in Mathematics Series. 388. 16-30 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Fujita: "On the rate of convergence of iterations in the domain-decomposition method" Proc.of 3rd Japan-China Joint Seminar on Numer.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujita: "Variational inequalitites for the Stokes equation with boundary conditions of friction type" Gakuto Intern.Series, Math.Sci.Appl.11. 15-33 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kawarada: "Numerical method for a free surface flow on the basis of the fictitious domain method" East-West J.of Numer.Math.5-1. 57-66 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kawarada: "Fuzzy optimazation method" Computational Science for 21st Century, Wiley. 643-651 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Kawarada: "Multi-start fuzzy optimazation method" Gakuto Intern.Series, Math.Sci.Appl.11.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Kawarada: "Wave motion breaking upon the shore" Gakuto Intern.Series, Math.Sci.Appl.11. 145-159 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Kawarada: "Wave Breaking Phenomenon on the Shore and Coastal Ecosystems" Abstracts of 4th Japan-china Sem.on Numer.Math.1-6 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujita: "Stability of some Navier-Stokes flows in doubly connected domains" Gakuto Intern.Series, Math.SciAppl.11. 116-125 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujita: "On the rate of convergence of iterations in the domain decomposition method" Proc.3rd China-Japan Semi.on Numer.Math.30-43 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Morimoto: "Stationary solutions for the Navier-Stokes equation and the Bousisinesq equations under general outflow condition" 数理解析研究所講究録. 1009. (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Morimoto: "Note on stationary Boussinesq equations in a bounded domain under general outflow condition" Proc.of NSEC6, 1997, Lithuania. (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Morimoto: "Perturbation of the Boussinesq flow in an annular domain with general outflow condition" Pitman Research Notes in Mathematics Series. 388. 66-75 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Morimoto: "General outflow condition for Naveier-Stokes flow" Kinokuniya Lec.Note in Numer.Appl.Anal.16. 209-224 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.Saito: "On the shape of domains and the speed of convergence in the certain DDM for the Stokes equation" Abstracts of 4th Japan-China Sem.on Numer.Math.25-28 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujita: "A remark on the existence of the Navier-Stokes flow with non-vanishing outflow condition" Gakuto Intern.Series, Math.Sci.Appl.vol.10. 53-61 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "Stability analysis of Navier-Stokes flows in annuli" Math.Meth.Appl.Sci.vol.20. 959-978 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kawarada: "Navier-Stokes flows coupled with potential flow through porous media" DDM in Sciences and Engineering, John Wiley. vol.8. 403-410 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "An analytical study of optimal speed of convergence of iterations in DDM under certain shape assumptions of domains" Computational Sciences for 21st Century, John Wiley. 139-148 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "On stationary solutions to Navier-Stokes quation in symmetric Plane domains under general outflow condition" Pitman Research Notes in Mathematics Series. vol.388. 16-30 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "On the rate of convergence of iterations in the domain-decomposition method" Proc.of 3rd Japan-China Joint Seminar on Num.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "Variational inequalitites for the Stokes equation with boundary conditions of friction type" Gakuto Intren.Series, Math.Sci.Appl.vol.11. 15-33 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kawarada: "Numerical method for a free surface flow on the basis of the fictitious domain method" East-West J.of Numer.Math.vol.5, No.1. 57-66 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kawarada: "Fuzzy optimazation method" Computational Science for 21st Century, Wiley. 643-651 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kawarada: "Multi-start fuzzy optimazation method" Gakuto Intern.Series, Math.Sci.Appl.vol.11.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kawarada: "Wave motion breaking upon the shore" Gakuto Intern.Series, Math.Sci.Appl.vol.11. 145-159 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Kawarada: "Wave Breaking Phenomenon on the Shore and Coastal Ecosystems" Abstracts of 4th Japan-China Sem.on Numer.Math.1-6 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "Stability of some Navier-Stokes flows in doubly connected domains" Gakuto Intern.Series.Math.Sci.Appl.vol.11. 116-125 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Fujita: "On the rate of convergence of iterations in the domain decomposition method" Proc.3rd China-Japan Semi.on Numer.Math.30-43 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Morimoto: "Stationary solutions for the Navier-Stokes equation and the Bousisinesqequations under general outflow condition" RIMS (Kyoto Univ.) Kokyuroku. vol.1009. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Morimoto: "Note on stationary Boussinesq equations in a bounded domain under general outflow condition" Proc.of NSEC 6. (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Morimoto: "Perturbation of the Boussinesq flow in an annular domain with general outflow condition" Pitman Research Notes in Mathematics Series. vol.388. 66-75 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Morimoto: "General outflow condition for Naveier-Stokes flow" Kinokuniya Lec.Note in Numer.Appl.Anal.vol.16. 209-224 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N.Saito: "On the shape of domains and the speed of convergence in the cerrain DDM for the Stokes equation" Abstracts of 4th Japan-China Sem on Numer.Math.25-28 (1998)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1999-12-08  

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