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Mathematical Theory of Error Analysis of Finite Element Methods

Research Project

Project/Area Number 14540122
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 InstitutionEhime University

Principal Investigator

TSUCHIYA Takuya  Ehime-U, Dept.Math.Sci, Professor, 理学部, 教授 (00163832)

Co-Investigator(Kenkyū-buntansha) SAKAGUTI Sigeru  Ehime-U, Dept.Math.Sci, Professor, 理学部, 教授 (50215620)
FANG Qing  Ehime-U, Dept.Math.Sci, Instructor, 理学部, 助手 (10243544)
Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordsfinite elements / error analysis / Galerkin methods / Mathematical foundation / 自由環境問題 / ダムの問題
Research Abstract

In this research project, we have tried to develop a mathematical theory of error analysis of finite element methods, and have obtained the following results.
(1)We have consider on error analysis of Galerkin methods applied to (non-) linear equations with a (linear or nonlinear) compact term defined in Hilbert space setting. We have found a simple way of developing mathematical theory of error analysis of Galerkin methods applied to such equations.
(2)We have proved rigorously the convergence of trial free boundary methods applied to the Dam Problem, which is a typical elliptic free boundary problem.
(3)We have consider on error analysis of the piecewise quadratic finite element method applied to 2-point boundary value problems defined on 1-dimensional bounded interval. We have found that all known error bounds are still valid even if coefficient function of the principle term is not-continuous or entirely positive.

Report

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

    (18 results)

All Other

All Publications (18 results)

  • [Publications] Q.Fang, T.Tsuchiya, T.Yamamoto: "Finite difference, finite element and finite volume methods applied to two-point boundary value problems"Journal of Computational and Applied Math. 139. 9-19 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Tsuchiya: "Finite element approximations of parametrized strongly nonlinear boundary value problems"Japan Journal of Industrial and Applied Mathematics. 19. 377-398 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuzawa, T.Suzuki, T.Ttsuchiya: "Finite elementapproximation of H-surfaces"Mathematics of Computation. 72. 607-617 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Isuchiya, K.Yoshida, Sae.Ishioka: "Yamamoto's principle and its applications to precise finite element error analysis"Journal of Computational and Applied Mathematics. 152. 507-532 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] T.Tsuchiya: "Precise finite element error analysis by Yamamoto's explicit inversion formula for tridiagonal matrices-"Numerische Mathematik. 94. 541-572 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Qing Fang, Takuya Tsuchiya, Tetsuro Yamamoto: "Finite difference, finite element and finite volume methods applied to two-point boundary value problems"Journal of Computational and Applied Mathematics. 139. 9-19 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takuya Tsuchiya: "Finite element approximations of parametrized strongly nonlinear boundary value problems"Japan Journal of Industrial and Applied Mathematics. 19. 377-398 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Yuki Matsuzawa, Takashi Suzuki, Takuya Tsuchiya: "Finite element approximation of H-surfaces"Mathematics of Computation. 72. 607-617 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takuya Tsuchiya, Kazuki Yoshida, Sae Ishioka: "Yamamoto's principle and its applications to precise finite element error analysis"Journal of Computational and Applied Mathematics. 152. 507-532 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Takuya Tsuchiya: "Precise finite element error analysis by Yamamoto s explicit inversion formula for tridiagonal matrices An extension of Babuska-Osborn's theorems"Numerische Mathematik. 94. 541-572 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2003 Final Research Report Summary
  • [Publications] Y.Matsuzawa, T.Suzuki, T.Tsuchiya: "Finite element approximation of H-surfaces"Math.Comp.. 72. 607-617 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Tsuchiya, K.Yoshida, S.Ishioka: "Yamamoto's principle and its applications to precise finite element error analysis"J.Comp.Appl.Math.. 152. 507-532 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Tsuchiya: "Precise finite element error analysis by Yamamoto's explicit inversion formula for tridiagonal matrices - an extension of Babuska-Osborn's theorems"Numerische Mathematik. 94. 541-572 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Fang, Tsuchiya, Yamamoto: "Finite difference finite element and finite volume methods applied to two-point boundary value problems"Journal of Computational and Applied Mathematics. 139. 9-19 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Tsuchiya: "Finite element approximations parametrized strongly nonlinear boundary value problems"Japan Journal of Industrial and Applied Mathematics. 19. 377-398 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Matsuzawa, Y., Suzuki, T., Tsuchiya, T.: "Finite element approximation of H-surfaces"Mathematics of Computation. 72. 607-617 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Tsuchiya, K.Yoshida, S.Ishioka: "Yamamoto's Principle and its applications to precise finite element error analysis"Japan Journal of Industrial and Applied Mathematics. 152. 507-532 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Tsuchiya: "Precise finite element error analysis by Yamamoto's explicit inversion formula for tridiagonal matrices"Numerische Mathematik. (to appear).

    • Related Report
      2002 Annual Research Report

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

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