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Research on high accuracy computing and numerical verification for Finite Element Method solution in a non-convex domain

Research Project

Project/Area Number 19740052
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKanazawa University

Principal Investigator

KOBAYSHI Kenta  Kanazawa University, 数物科学系, 准教授 (60432902)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,800,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥600,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywords精度保証 / 有限要素法 / 誤差評価 / 非凸領域 / ポアソン方程式 / 重調和方程式 / Navier-Stokes方程式 / ボアソン方程式
Research Abstract

In solving partial differential equation by Finite Element Method in a non-convex domain, it is known that the convergent rate could be improved by adding singularity functions to the Finite Element basis or using mesh refinement. In our research, we have obtained explicit error estimations for these problems. These results can be applied for computer-assisted proof for non-linear problems.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (35 results)

All 2010 2009 2008 2007 Other

All Journal Article (9 results) (of which Peer Reviewed: 7 results) Presentation (26 results)

  • [Journal Article] A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions2009

    • Author(s)
      K. Kobayashi
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics Vol.26[2/3]

      Pages: 493-516

    • NAID

      10028169365

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the critical case of Okamoto's continuous non-differentiable functions2009

    • Author(s)
      K. Kobayashi
    • Journal Title

      Proceedings of the Japan Academy, Series A Vol.85[8]

      Pages: 101-104

    • NAID

      120005447707

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the critical case of Okamoto's continuous non-differentiable functions2009

    • Author(s)
      Kenta Kobayashi
    • Journal Title

      Proceedings of the Japan Academy, Series A 85[8]

      Pages: 101-104

    • NAID

      120005447707

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions2009

    • Author(s)
      Kenta Kobayashi
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 26[2/3]

      Pages: 493-516

    • NAID

      10028169365

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions2009

    • Author(s)
      Kobayashi, K
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics Vol.26(掲載決定)

    • NAID

      10028169365

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] メッシュリファイメントを用いた有限要素解の事前誤差評価2008

    • Author(s)
      小林健太
    • Journal Title

      京都大学数理解析研究所講究録 Vol.1614

      Pages: 180-186

    • Related Report
      2009 Final Research Report
  • [Journal Article] Verified numerical computation of solutions for the stationary Navier-Stokes equation in nonconvex polygonal domains2007

    • Author(s)
      K. Hashimoto, K. Kobayashi, M.T. Nakao
    • Journal Title

      Hokkaido Mathematical Journal vol.36[4]

      Pages: 777-799

    • Related Report
      2009 Final Research Report
  • [Journal Article] Verified numerical computation of solutions for the stationary Navier-Stokes equation in nonconvex polygonal domains2007

    • Author(s)
      Nakao, M. T.; Hashimoto, K.; Kobayasbi, K.
    • Journal Title

      Hokkaido Mathematical Journal 36

      Pages: 777-799

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the global uniqueness of Stokes' wave of extreme form

    • Author(s)
      K. Kobayashi
    • Journal Title

      IMA Journal of Applied Mathematics (掲載決定)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Presentation] On the interpolation constant over triangular elements2010

    • Author(s)
      Kenta Kobayashi
    • Organizer
      International Workshop on Numerical Verification and its Applications 2010 (INVA2010)
    • Place of Presentation
      Hotel Lido Azzurro(Tokyo)
    • Year and Date
      2010-03-13
    • Related Report
      2009 Final Research Report
  • [Presentation] On the interpolation constant over triangular elements2010

    • Author(s)
      Kenta Kobayashi
    • Organizer
      International Workshop on Numerical Verification and its Applications 2010(INVA2010)
    • Place of Presentation
      Hotel Lido Azzurro, Hachijo-jima(東京都)
    • Year and Date
      2010-03-13
    • Related Report
      2009 Annual Research Report
  • [Presentation] 三角形領域上の補間誤差定数について2010

    • Author(s)
      小林健太
    • Organizer
      北陸応用数理研究会2010
    • Place of Presentation
      金沢大学サテライト・プラザ(石川県)
    • Year and Date
      2010-02-12
    • Related Report
      2009 Final Research Report
  • [Presentation] An a priori constant which appear in bi-harmonic problems2009

    • Author(s)
      Kenta Kobayashi
    • Organizer
      Dagstuhl Seminar: Computer-assisted proofs - tools, methods and applications
    • Place of Presentation
      Schloss Dagstuhl(Germany)
    • Year and Date
      2009-11-18
    • Related Report
      2009 Final Research Report
  • [Presentation] An a priori constant which appear in bi-harmonic problems2009

    • Author(s)
      Kenta Kobayashi
    • Organizer
      Dagstuhl Seminar : Computer-assisted proofs-tools, methods and applications
    • Place of Presentation
      Schloss Dagstuhl, Wadern,(ドイツ)Germany
    • Year and Date
      2009-11-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] A constructive a priori error estimation for finite element discretizations in a non-convex domain using mesh refinement2009

    • Author(s)
      Kenta Kobayashi
    • Organizer
      International Conference on Engineering and Computational Mathematics (ECM2009)
    • Place of Presentation
      The Hong Kong Polytechnic University(China)
    • Year and Date
      2009-05-28
    • Related Report
      2009 Final Research Report
  • [Presentation] A constructive a priori error estimation for finite element discretizations in a non-convex domain using mesh refinement2009

    • Author(s)
      Kenta Kobayashi
    • Organizer
      International Conference on Engineering and Computational Mathematics(ECM2009)
    • Place of Presentation
      The Hong Kong Polytechnic(中国)University
    • Year and Date
      2009-05-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] An a priori constant which appears in bi-harmonic problems2009

    • Author(s)
      Kenta Kobayashi
    • Organizer
      International Workshop on Numerical Verification and its Applications 2009 (INVA2009)
    • Place of Presentation
      Hotel Breeze Bay Marina(Okinawa)
    • Year and Date
      2009-03-24
    • Related Report
      2009 Final Research Report
  • [Presentation] An a priori constant which appears in bi-harmonic problems2009

    • Author(s)
      Kobayashi, K
    • Organizer
      International Workshop on Numerical Verification and its Applications 2009
    • Place of Presentation
      Hotel Breeze Bay Marina, Mivako Island, Okinawa
    • Year and Date
      2009-03-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Numerical verification method and its applications2009

    • Author(s)
      小林健太
    • Organizer
      第10回北東数学解析研究会
    • Place of Presentation
      東北大学理学部(宮城県)
    • Year and Date
      2009-02-17
    • Related Report
      2009 Final Research Report
  • [Presentation] A constructive a priori error estimation for finite element discretizations in a non-convex domain using a mesh refinement2009

    • Author(s)
      Kenta Kobayashi
    • Organizer
      1st African Conference on Computational Mechanics (AfriCOMP 2009)
    • Place of Presentation
      Sun City Convention Center(South Africa)
    • Year and Date
      2009-01-07
    • Related Report
      2009 Final Research Report
  • [Presentation] A constructive a priori error estimation for finite element discretizations in a non-convex domain using mesh refinement2009

    • Author(s)
      Kobayashi, K
    • Organizer
      1st African Conference on Computational Mechanics
    • Place of Presentation
      Sun City, South Africa
    • Year and Date
      2009-01-07
    • Related Report
      2008 Annual Research Report
  • [Presentation] 三角形要素上の補間誤差定数について2008

    • Author(s)
      小林健太
    • Organizer
      流れ問題のための高品質数値解法と計算機援用解析学
    • Place of Presentation
      KKRホテル金沢(石川県)
    • Year and Date
      2008-11-18
    • Related Report
      2009 Final Research Report
  • [Presentation] 非凸領域における有限要素法の事前誤差評価について2008

    • Author(s)
      小林健太
    • Organizer
      第3回岐阜非線形ワークショップ-計算科学の基盤としての数値解析-
    • Place of Presentation
      岐阜大学地域科学部棟(岐阜県)
    • Year and Date
      2008-10-27
    • Related Report
      2009 Final Research Report
  • [Presentation] A constructive a priori error estimation for finite element discretizations in a non-convex domain using mesh refinement2008

    • Author(s)
      Kenta Kobayashi
    • Organizer
      International Workshop on Numerical Verification and its Applications 2008 (INVA2008)
    • Place of Presentation
      Tokyo Dai-ichi Hotel OKINAWA GRAND MER RESORT(Okinawa)
    • Year and Date
      2008-03-06
    • Related Report
      2009 Final Research Report
  • [Presentation] メッシュリファイメントを用いた有限要素解の事前誤差評価2007

    • Author(s)
      小林健太
    • Organizer
      研究集会:計算科学の基盤技術としての高速アルゴリズムとその周辺
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2007-11-16
    • Related Report
      2009 Final Research Report
  • [Presentation] メッシュリファイメントを用いた有限要素解の事前誤差評価2007

    • Author(s)
      小林 健太
    • Organizer
      RIMS研究集会:計算科学の基盤技術としての高速アルゴリズムとその周辺
    • Place of Presentation
      京都大学 数理解析研究所
    • Year and Date
      2007-11-16
    • Related Report
      2007 Annual Research Report
  • [Presentation] A constructive a priori error estimation for finite element discretizations in a non-convex domain using mesh refinement2007

    • Author(s)
      Kenta Kobayashi
    • Organizer
      The 3rd East Asia SIAM Conference
    • Place of Presentation
      Xiamen University(China)
    • Year and Date
      2007-11-03
    • Related Report
      2009 Final Research Report
  • [Presentation] A Constructive a Priori Error Estimation for Finite Element Discretizations in a Non-convex Domain Using Mesh Refinement2007

    • Author(s)
      Kobayashi, K.
    • Organizer
      The 3rd East Asia SIAM Conference
    • Place of Presentation
      Xiamen, China
    • Year and Date
      2007-11-03
    • Related Report
      2007 Annual Research Report
  • [Presentation] Michael Plum, Some numerical results for the explicit L∞error bounds2007

    • Author(s)
      Kenta Kobayashi
    • Organizer
      COE Conference on the Development of Dynamic Mathematics with High Functionality (DMHF2007)
    • Place of Presentation
      Fukuoka Recent Hotel(Fukuoka)
    • Year and Date
      2007-10-04
    • Related Report
      2009 Final Research Report
  • [Presentation] Some numerical results for the explicit L∞ error bounds2007

    • Author(s)
      Kobayashi, K.
    • Organizer
      Conference on the Development of Dynamic Mathematics with High Functionality
    • Place of Presentation
      Fukuoka, Japan
    • Year and Date
      2007-10-04
    • Related Report
      2007 Annual Research Report
  • [Presentation] 水面波方程式に対する計算機援用証明2007

    • Author(s)
      小林健太
    • Organizer
      日本数学会2007年度秋季総合分科会
    • Place of Presentation
      東北大学川内北キャンパス(宮城県)
    • Year and Date
      2007-09-23
    • Related Report
      2009 Final Research Report
  • [Presentation] A constructive a priori error estimation for finite element discretizations in a non-convex domain using mesh refinement2007

    • Author(s)
      Kenta Kobayashi
    • Organizer
      Conference on Inequalities and Applications '07
    • Place of Presentation
      De La Motte Castle(Hungary)
    • Year and Date
      2007-09-11
    • Related Report
      2009 Final Research Report
  • [Presentation] A Constructive a Priori Error Estimation for Finite Element Discretizations in a Non-convex Domain Using Mesh Refinement2007

    • Author(s)
      Kobayashi, K.
    • Organizer
      Conference on Inequalities and Applications '07
    • Place of Presentation
      Noszvaj, Hungary
    • Year and Date
      2007-09-11
    • Related Report
      2007 Annual Research Report
  • [Presentation] A constructive a priori error estimation for finite element discretizations in a non-convex domain using mesh refinement2007

    • Author(s)
      Kenta Kobayashi
    • Organizer
      International Conference on Recent Developments of Numerical Schemes for Flow Problems (INSF2007)
    • Place of Presentation
      Kyushu University Nishijin Plaza(Fukuoka)
    • Year and Date
      2007-06-29
    • Related Report
      2009 Final Research Report
  • [Presentation] A Constructive a Priori Error Estimation for Finite Element Discretizations in a Non-convex Domain Using Mesh Refinement2007

    • Author(s)
      Kobayashi, K.
    • Organizer
      International Conference on Recent Developments of Numerical Schemes for Flow Problems
    • Place of Presentation
      Kyushu University
    • Year and Date
      2007-06-29
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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