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Advanced research on the Numerical verification Method based on the Finite Element Method

Research Project

Project/Area Number 16H03950
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionHitotsubashi University

Principal Investigator

KOBAYASHI Kenta  一橋大学, 大学院経営管理研究科, 教授 (60432902)

Co-Investigator(Kenkyū-buntansha) 土屋 卓也  愛媛大学, 理工学研究科(理学系), 教授 (00163832)
渡部 善隆  九州大学, 情報基盤研究開発センター, 准教授 (90243972)
劉 雪峰  新潟大学, 自然科学系, 准教授 (50571220)
高安 亮紀  筑波大学, システム情報系, 助教 (60707743)
Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥17,680,000 (Direct Cost: ¥13,600,000、Indirect Cost: ¥4,080,000)
Fiscal Year 2019: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2018: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2016: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Keywords精度保証付き数値計算 / 有限要素法 / 誤差評価 / 補間誤差解析 / 補間誤差評価 / 固有値問題 / 補間誤差定数
Outline of Final Research Achievements

In this research, we have conducted the studies for the further improvements on the Numerical Verification Method based on the Finite Element Method. Specifically, we were able to make progress on the error analysis of both conforming and non-conforming Finite Element Methods based on the interpolation error analysis, on the improved method for verifying the existence and bounds of the inverse of the elliptic linear operator, and on the method of applying them to the actual non-linear partial differential equations.

Academic Significance and Societal Importance of the Research Achievements

精度保証付き数値計算は近年、数値計算結果の品質保証だけでなく、偏微分方程式の解の存在証明など、数学的に厳密な証明などにも用いられており、応用範囲が広がっています。精度保証付き数値計算のうちでも有限要素法をベースにした方法は、関数解析の理論を用いることで効率的な手法の構築が可能という利点があります。本研究では、有限要素法をベースにした精度保証付き数値計算について、より効率的な手法や、今まで適用できなかった問題にも適用できる手法を開発する、などの成果をあげることができました。

Report

(5 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • Research Products

    (110 results)

All 2020 2019 2018 2017 2016

All Journal Article (24 results) (of which Int'l Joint Research: 8 results,  Peer Reviewed: 24 results,  Open Access: 7 results,  Acknowledgement Compliant: 5 results) Presentation (85 results) (of which Int'l Joint Research: 47 results,  Invited: 18 results) Book (1 results)

  • [Journal Article] Error analysis of Lagrange interpolation on tetrahedrons2020

    • Author(s)
      Kobayashi Kenta、Tsuchiya Takuya
    • Journal Title

      Journal of Approximation Theory

      Volume: 249 Pages: 105302-105302

    • DOI

      10.1016/j.jat.2019.105302

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearity"2020

    • Author(s)
      K. Matsue and A. Takayasu
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 374 Pages: 112607-112607

    • DOI

      10.1016/j.cam.2019.112607

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces2019

    • Author(s)
      Kinoshita Takehiko、Watanabe Yoshitaka、Nakao Mitsuhiro T.
    • Journal Title

      Journal of Differential Equations

      Volume: 266 Issue: 9 Pages: 5431-5447

    • DOI

      10.1016/j.jde.2018.10.027

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space2019

    • Author(s)
      Watanabe Yoshitaka、Kinoshita Takehiko、Nakao Mitsuhiro T.
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 印刷中 Issue: 2 Pages: 407-420

    • DOI

      10.1007/s13160-019-00344-8

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A computer‐assisted method for the diblock copolymer model2019

    • Author(s)
      Cai Shuting、Watanabe Yoshitaka
    • Journal Title

      ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f?r Angewandte Mathematik und Mechanik

      Volume: 99 Issue: 7 Pages: 1-1

    • DOI

      10.1002/zamm.201800125

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Reorganizing topologies of Steiner trees to accelerate their eliminations2019

    • Author(s)
      Grodet Aymeric、Tsuchiya Takuya
    • Journal Title

      Discrete Mathematics, Algorithms and Applications

      Volume: 12 Issue: 01 Pages: 2050003-2050003

    • DOI

      10.1142/s1793830920500032

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Guaranteed Eigenvalue Bounds for the Steklov Eigenvalue Problem2019

    • Author(s)
      You Chun'guang、Xie Hehu、Liu Xuefeng
    • Journal Title

      SIAM Journal on Numerical Analysis

      Volume: 57 Issue: 3 Pages: 1395-1410

    • DOI

      10.1137/18m1189592

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Rigorous numerical computations for 1D advection equations with variable coefficients2019

    • Author(s)
      A. Takayasu, S. Yoon, and Y. Endo
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 36 Issue: 2 Pages: 357-384

    • DOI

      10.1007/s13160-019-00345-7

    • NAID

      120007133327

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Error analysis of Crouzeix?Raviart and Raviart?Thomas finite element methods2018

    • Author(s)
      Kobayashi Kenta、Tsuchiya Takuya
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 35 Issue: 3 Pages: 1191-1211

    • DOI

      10.1007/s13160-018-0325-9

    • NAID

      210000166840

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Explicit estimation of error constants appearing in non-conforming linear triangular finite element method2018

    • Author(s)
      Liu Xuefeng、Kikuchi Fumio
    • Journal Title

      Applications of Mathematics

      Volume: 63 Issue: 4 Pages: 381-397

    • DOI

      10.21136/am.2018.0097-18

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Explicit finite element error estimates for nonhomogeneous Neumann problems2018

    • Author(s)
      Li Qin、Liu Xuefeng
    • Journal Title

      Applications of Mathematics

      Volume: 63 Issue: 3 Pages: 367-379

    • DOI

      10.21136/am.2018.0095-18

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Approximating surface areas by interpolations on triangulations2017

    • Author(s)
      Kenta KOBAYASHI, Takuya TSUCHIYA
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 34 Issue: 2 Pages: 509-530

    • DOI

      10.1007/s13160-017-0253-0

    • NAID

      210000174791

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations2017

    • Author(s)
      Watanabe Yoshitaka、Nakao Mitsuhiro T.、Nagatou Kaori
    • Journal Title

      JSIAM Letters

      Volume: 9 Issue: 0 Pages: 77-80

    • DOI

      10.14495/jsiaml.9.77

    • NAID

      130006252917

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Validated constructive error estimations for biharmonic problems2017

    • Author(s)
      Takehiko Kinoshita, Yoshitaka Watanabe, and Mitsuhiro T. Nakao
    • Journal Title

      Reliable Computing

      Volume: 25 Pages: 168-177

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Accurate method of verified computing for solutions of semilinear heat equations2017

    • Author(s)
      Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, and Shin’ichi Oishi
    • Journal Title

      Reliable computing

      Volume: 25 Pages: 74-99

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A method of verified computations for solutions to semilinear parabolic equations using semigroup theory2017

    • Author(s)
      M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi
    • Journal Title

      SIAM Journal on Numerical Analysis

      Volume: 55:2 Issue: 2 Pages: 980-1001

    • DOI

      10.1137/141001664

    • NAID

      120007129016

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Numerical verification for existence of a global-in-time solution to semilinear parabolic equations2017

    • Author(s)
      M. Mizuguchi, A. Takayasu, T. Kubo, and S. Oishi
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 315 Pages: 1-16

    • DOI

      10.1016/j.cam.2016.10.024

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A recursive formula for the circumradius of the n-simplex2016

    • Author(s)
      Kenta Kobayashi
    • Journal Title

      Forum Geometricorum

      Volume: 16 Pages: 179-184

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Extending Babuska-Aziz's theorem to higher-order Lagrange interpolation2016

    • Author(s)
      K. Kobayashi, T. Tsuchiya
    • Journal Title

      Applications of Mathematics

      Volume: 61 Issue: 2 Pages: 121-133

    • DOI

      10.1007/s10492-016-0125-y

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] First and second Hadamard variational formulae of the Green function for general domain perturbations2016

    • Author(s)
      Takashi Suzuki and Takuya Tsuchiya
    • Journal Title

      Journal of Mathematical Society of Japan

      Volume: 68 Pages: 1389-1419

    • NAID

      130005433299

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Norm bound computation for inverses of linear operators in Hilbert spaces2016

    • Author(s)
      Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, and Mitsuhiro T. Nakao
    • Journal Title

      Journal of Differential Equations

      Volume: 260 Issue: 7 Pages: 6363-6374

    • DOI

      10.1016/j.jde.2015.12.041

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid2016

    • Author(s)
      Yoshitaka Watanabe
    • Journal Title

      Journal of Computational and Applied Mathematics

      Volume: 302 Pages: 157-170

    • DOI

      10.1016/j.cam.2016.01.055

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains2016

    • Author(s)
      Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, and Mitsuhiro T. Nakao
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 33 Issue: 3 Pages: 629-636

    • DOI

      10.1007/s13160-016-0223-y

    • NAID

      210000183342

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the embedding constant of the Sobolev type inequality for fractional derivatives2016

    • Author(s)
      Makoto Mizuguchi, Akitoshi Takayasu, Takayuki Kubo, and Shin'ichi Oishi
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 7 Issue: 3 Pages: 386-394

    • DOI

      10.1587/nolta.7.386

    • NAID

      130005161829

    • ISSN
      2185-4106
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Presentation] Computer-assisted proofs for the Orr-Sommerfeld equation2019

    • Author(s)
      Yoshitaka Watanabe
    • Organizer
      Workshop: Rigorous Computational Dynamics in Infinite Dimensions
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Rigorous integrator for nonlinear heat equations in the complex plane of time using semigroup theory2019

    • Author(s)
      Akitoshi Takayasu
    • Organizer
      Workshop: Rigorous Computational Dynamics in Infinite Dimensions
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Numerical validation of periodic orbit to delay differential equations via Newton-Kantorovich argument2019

    • Author(s)
      Akitoshi Takayasu
    • Organizer
      The 1st Hungary-Japan Workshop on Delay Equations and Mathematical Epidemiology
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 極小曲面の有限要素近似について2019

    • Author(s)
      土屋卓也
    • Organizer
      第24回計算工学講演会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Global existence of a solution for the nonlinear heat equation in the complex plane of time2019

    • Author(s)
      高安亮紀
    • Organizer
      RIMS 共同研究 (公開型)「偏微分方程式の臨界現象と正則性理論及び漸近解析」
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Rigorous numerics for nonlinear heat equations in the complex plane of time2019

    • Author(s)
      Akitoshi Takayasu
    • Organizer
      Equadiff 2019
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The circumradius condition and its application2019

    • Author(s)
      Kenta Kobayashi
    • Organizer
      International Congress on Industrial and Applied Mathematics (ICIAM2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Error analysis of Raviart-Thomas and Crouzeix-Raviart finite element methods on non-regular meshes2019

    • Author(s)
      Takuya Tsuchiya
    • Organizer
      International Congress on Industrial and Applied Mathematics (ICIAM2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A computer-assisted proof of the critical Reynolds number for the Orr-Sommerfeld equation2019

    • Author(s)
      Yoshitaka Watanabe
    • Organizer
      International Congress on Industrial and Applied Mathematics (ICIAM2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Numerical validation of blow-up solutions of ODEs2019

    • Author(s)
      Akitoshi Takayasu
    • Organizer
      International Congress on Industrial and Applied Mathematics (ICIAM2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Rigorous numerics for a singular solution of advection equations with variable coefficients2019

    • Author(s)
      Akitoshi Takayasu
    • Organizer
      International Congress on Industrial and Applied Mathematics (ICIAM2019)
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] H10射影誤差に対する2次の誤差評価の最良定数の包含方法について2019

    • Author(s)
      木下 武彦, 渡部 善隆, 山本 野人, 中尾 充宏
    • Organizer
      日本応用数理学会2019年度年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Gaussの超幾何微分方程式のモノドロミー行列に対する精度保証付き数値計算2019

    • Author(s)
      井上直也, 石毛利昌, 高安亮紀
    • Organizer
      日本応用数理学会2019年度年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] チェビシェフ級数を用いたタイムステッピングによる常微分方程式系の精度保証付き数値解法2019

    • Author(s)
      舩越康太, 高安亮紀
    • Organizer
      日本応用数理学会2019年度年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] H10関数の直交多項式近似に対する2次の誤差評価の最良定数について2019

    • Author(s)
      木下武彦, 渡部善隆, 山本野人, 中尾充宏
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Computer-assisted proofs for a nonlinear heat equation in the complex plane of time2019

    • Author(s)
      Akitoshi Takayasu
    • Organizer
      CRM Applied Mathematics Seminars
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Nakao et al. (2005) 最後の謎2019

    • Author(s)
      木下武彦, 渡部善隆, 中尾充宏
    • Organizer
      第3回精度保証付き数値計算の実問題への応用研究集会(NVR 2019)
    • Related Report
      2019 Annual Research Report
  • [Presentation] ある楕円型境界値問題から導かれる近似作用素のノルムの収束性2019

    • Author(s)
      木下武彦, 渡部善隆, 中尾充宏
    • Organizer
      応用数学合同研究集会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Error analysis of Crouzeix-Raviart finite element method on non-regular meshes2019

    • Author(s)
      土屋卓也
    • Organizer
      日本応用数理学会環瀬戸内研究部会2019年度シンポジウム
    • Related Report
      2019 Annual Research Report
  • [Presentation] Poisson方程式に対する構成的高次誤差評価とその応用2019

    • Author(s)
      渡部善隆, 木下武彦, 山本野人, 中尾充宏
    • Organizer
      日本数学会2019年年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 複素Ginzburg-Landau方程式に対する解の精度保証付き数値計算2019

    • Author(s)
      高安亮紀
    • Organizer
      日本数学会2019年年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Poisson方程式に対する構成的高次誤差評価2019

    • Author(s)
      渡部善隆, 木下武彦, 山本野人, 中尾充宏
    • Organizer
      日本応用数理学会2019年研究部会連合発表会
    • Related Report
      2018 Annual Research Report
  • [Presentation] チェビシェフ級数を用いた非線形常微分方程式系の精度保証付き数値解法2019

    • Author(s)
      舩越康太, 高安亮紀
    • Organizer
      日本応用数理学会2019年研究部会連合発表会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 時間発展方程式の線形化問題に対する解作用素の厳密評価2019

    • Author(s)
      高安亮紀
    • Organizer
      日本応用数理学会2019年研究部会連合発表会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 一般化エルミート固有値問題の部分固有値計算における周回積分に基づく精度保証法の改良2019

    • Author(s)
      今倉暁, 保國惠一, 高安亮紀
    • Organizer
      日本応用数理学会2019年研究部会連合発表会
    • Related Report
      2018 Annual Research Report
  • [Presentation] A remark on L2-error estimations for FEM solutions on non-convex domains2019

    • Author(s)
      Kenta Kobayashi
    • Organizer
      Numerical Verification (NIVEA) 2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Error estimation of Lagrange interpolation without the shape-regularity assumption2019

    • Author(s)
      Takuya Tsuchiya
    • Organizer
      Numerical Verification (NIVEA) 2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Rigorous spectral methods for initial value problems of ordinary differential equations2019

    • Author(s)
      Akitoshi Takayasu
    • Organizer
      Numerical Verification (NIVEA) 2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The circumradius condition and its application2019

    • Author(s)
      Kenta Kobayashi
    • Organizer
      Australia New Zealand Industrial and Applied Mathematics 55th Annual Conference (ANZIAM 2019)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Hadamard variational fomulae and its applications for iterative numerical schemes2019

    • Author(s)
      Takuya Tsuchiya
    • Organizer
      Australia New Zealand Industrial and Applied Mathematics 55th Annual Conference (ANZIAM 2019)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 正則性条件を仮定しないLagrange補間の誤差評価について2018

    • Author(s)
      土屋卓也
    • Organizer
      日本応用数理学会 環瀬戸内応用数理研究部会シンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] The essence of numerical verification methods for PDEs2018

    • Author(s)
      Yoshitaka Watanabe
    • Organizer
      2018 Workshop on Recent views of Nonlinear Analysis
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 反復解法における誤差履歴2018

    • Author(s)
      渡部善隆
    • Organizer
      第2回精度保証付き数値計算の実問題への応用研究集会(NVR 2018)
    • Related Report
      2018 Annual Research Report
  • [Presentation] 非線形熱方程式の複素時間における解の精度保証付き数値計算2018

    • Author(s)
      高安亮紀
    • Organizer
      京都大学数理解析研究所RIMS研究集会「次世代の科学技術を支える数値解析学の基盤整備と応用展開」
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 2階線形楕円型作用素に対する可逆性検証と精度保証付きノルム評価の改善2018

    • Author(s)
      渡部善隆, 木下武彦, 中尾充宏
    • Organizer
      日本数学会2018年度秋季総合分科会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 2階楕円型作用素に対する逆作用素ノルム評価の改良2018

    • Author(s)
      渡部善隆, 木下武彦, 中尾充宏
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 微分方程式の爆発解の精度保証付き数値計算:指数関数非線型項を持つ場合2018

    • Author(s)
      松江要, 高安亮紀
    • Organizer
      日本数学会2018年度秋季総合分科会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 非線形熱方程式の複素時間における解の挙動:精度保証付き数値計算によるアプローチ2018

    • Author(s)
      高安亮紀
    • Organizer
      大分微分方程式研究集会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] フーリエ係数の時間発展方程式に対する解の精度保証付き数値計算2018

    • Author(s)
      高安亮紀
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 微分方程式の爆発解の精度保証付き数値計算:ケーススタディ - 指数関数非線型項を持つ場合2018

    • Author(s)
      松江要, 高安亮紀
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 一般化エルミート固有値問題の周回積分型精度保証付き部分固有値計算2018

    • Author(s)
      今倉暁, 保國惠一, 高安亮紀
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] A higher order error estimation for finite element approximations of the Poisson equation2018

    • Author(s)
      Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto and Mitsuhiro T. Nakao
    • Organizer
      18th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Verified computations of eigenvalue exclosures for linearized Kolmogorov problem2018

    • Author(s)
      Yoshitaka Watanabe, Michael Plum, Kaori Nagatou and Mitsuhiro T. Nakao
    • Organizer
      18th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Generation of C_0 semigroup on sequence spaces for rigorous spectral methods in PDEs2018

    • Author(s)
      Akitoshi Takayasu, Motohiro Sobajima
    • Organizer
      18th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Verified computing for partial eigenvalues using a contour integral-type eigensolver2018

    • Author(s)
      Akitoshi Takayasu, Akira Imakura, Keiichi Morikuni
    • Organizer
      18th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2018)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Error analysis of Crouzeix-Raviart and Raviart-Thomas finite element methods2018

    • Author(s)
      土屋卓也
    • Organizer
      環瀬戸内ワークショップ
    • Related Report
      2018 Annual Research Report
  • [Presentation] Error analysis of Crouzeix-Raviart and Raviart-Thomas finite element methods2018

    • Author(s)
      Takuya Tsuchiya
    • Organizer
      SIAM East Asian Section Conference 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Crouzeix--Raviart有限要素法と Raviart-Thomas有限要素法の誤差解析2018

    • Author(s)
      土屋卓也
    • Organizer
      計算工学講演会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Verified partial eigenvalue computation for generalized Hermitian eigenproblems using contour integrals2018

    • Author(s)
      今倉暁, 保國惠一, 高安亮紀
    • Organizer
      第47回数値解析シンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] The relation between Crouzeix-Raviart and Raviart-Thomas finite element methods2018

    • Author(s)
      Kenta Kobayashi
    • Organizer
      International Workshop on Numerical Methods for Partial Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The relation between Crouzeix-Raviart and Raviart-Thomas finite element methods2018

    • Author(s)
      Kenta Kobayashi
    • Organizer
      Australia New Zealand Industrial and Applied Mathematics 54th Annual Conference (ANZIAM2018)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A higher order error estimation of the Poisson equation and its applications2018

    • Author(s)
      Yoshitaka Watanabe
    • Organizer
      International Workshop on Numerical Methods for Partial Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A priori error estimation for the finite element solution to Stokes equation in 3D domain2018

    • Author(s)
      Xuefeng Liu
    • Organizer
      International Workshop on Numerical Methods for Partial Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Error analysis of Lagrange interpolation on tetrahedrons2017

    • Author(s)
      Kenta Kobayashi, Takuya Tsuchiya
    • Organizer
      The second Vietnam International Applied Mathematics Conference (VIAMC 2017)
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Error analysis of Lagrange interpolation on tetrahedrons2017

    • Author(s)
      Kenta Kobayashi, Takuya Tsuchiya
    • Organizer
      Workshop on Free Boundary Problems and Nonlinear PDEs
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Some computer-assisted proofs for the Navier-Stokes equations2017

    • Author(s)
      Yoshitaka Watanabe
    • Organizer
      Rigorous Numerics for Infinite Dimensional Nonlinear Dynamics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Verified computations for solutions to 1-dimensional advection equations with variable coefficients2017

    • Author(s)
      Akitoshi Takayasu
    • Organizer
      Dagstuhl Seminar
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Approximating surface areas by interpolations on triangulations2017

    • Author(s)
      小林健太, 土屋卓也
    • Organizer
      日本数学会2017年度年会
    • Place of Presentation
      首都大学東京南大沢キャンパス(東京都八王子市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] あるコンパクト作用素のレゾルベントに対する下側評価について2017

    • Author(s)
      木下武彦, 渡部善隆, 中尾充宏
    • Organizer
      日本数学会2017年度年会
    • Place of Presentation
      首都大学東京南大沢キャンパス(東京都八王子市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] Error analysis of Lagrange interpolation on tetrahedrons2017

    • Author(s)
      Kenta Kobayashi, Takuya Tsuchiya
    • Organizer
      International Workshop on Numerical Verification and its Applications 2017 (INVA2017)
    • Place of Presentation
      Hotel Breeze Bay Marina, Miyako Island, Okinawa
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Approximating surface area by interpolations on triangulations2017

    • Author(s)
      Kenta Kobayashi, Takuya Tsuchiya
    • Organizer
      International Workshop on Numerical Verification and its Applications 2017 (INVA2017)
    • Place of Presentation
      Hotel Breeze Bay Marina, Miyako Island, Okinawa
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An alternative approach of invertibility verifications for linear operators in Hilbert spaces2017

    • Author(s)
      Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
    • Organizer
      International Workshop on Numerical Verification and its Applications 2017 (INVA2017)
    • Place of Presentation
      Hotel Breeze Bay Marina, Miyako Island, Okinawa
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Some remarks on the numerical norm estimation of the inverse operator in Hilbert spaces2017

    • Author(s)
      Mitsuhiro T. Nakao, Takehiko Kinoshita, Yoshitaka Watanabe
    • Organizer
      International Workshop on Numerical Verification and its Applications 2017 (INVA2017)
    • Place of Presentation
      Hotel Breeze Bay Marina, Miyako Island, Okinawa
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] High-preicision eigenvalue bounds for biharmonic differential operators2017

    • Author(s)
      Xuefeng Liu
    • Organizer
      International Workshop on Numerical Verification and its Applications 2017 (INVA2017)
    • Place of Presentation
      Hotel Breeze Bay Marina, Miyako Island, Okinawa
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Numerical validation of blow-up solutions via quasi-parabolic compactifications2017

    • Author(s)
      Akitoshi Takayasu, Kaname Matsue
    • Organizer
      International Workshop on Numerical Verification and its Applications 2017 (INVA2017)
    • Place of Presentation
      Hotel Breeze Bay Marina, Miyako Island, Okinawa
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] スペクトル法を用いた変数係数1次元移流方程式の精度保証付き解法2017

    • Author(s)
      尹授老, 高安亮紀
    • Organizer
      日本応用数理学会第13回研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都調布市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] Approximating surface areas by interpolations on triangulations2017

    • Author(s)
      小林健太, 土屋卓也
    • Organizer
      日本応用数理学会第13回研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都調布市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] Error analysis of Lagrange interpolation on tetrahedrons2017

    • Author(s)
      Kenta Kobayashi
    • Organizer
      Australia New Zealand Industrial and Applied Mathematics 53th Annual Conference (ANZIAM 2017)
    • Place of Presentation
      The Adelaide Hills Convention Centre, Hahndorf, Australia
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Computable norm bounds of the evolution operator using spectral properties2016

    • Author(s)
      Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, and Shin'ichi Oishi
    • Organizer
      The 35th JSST Annual Conference International Conference on Simulation Technology (JSST2016)
    • Place of Presentation
      Kyoto University, Kyoto, Japan
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Error Analysis of Lagrange Interpolation on Tetrahedrons2016

    • Author(s)
      Kenta Kobayashi, Takuya Tsuchiya
    • Organizer
      17th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2016)
    • Place of Presentation
      Uppsala University, Sweden
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Validated constructive error estimatations for bi-harmonic problems2016

    • Author(s)
      Yoshitaka Watanabe, Takehiko Kinoshita, and Mitsuhiro T. Nakao
    • Organizer
      17th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2016)
    • Place of Presentation
      Uppsala University, Sweden
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On verification methods for parabolic partial differential equations using the evolution operator2016

    • Author(s)
      Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, and Shin'ichi Oishi
    • Organizer
      17th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2016)
    • Place of Presentation
      Uppsala University, Sweden
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Verified numerical computations for blow-up solutions of ODEs2016

    • Author(s)
      Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shin'ichi Oishi
    • Organizer
      17th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2016)
    • Place of Presentation
      Uppsala University, Sweden
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A framework for highprecision verified eigenvalue bounds by using finite element methods2016

    • Author(s)
      Xuefeng Liu
    • Organizer
      17th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2016)
    • Place of Presentation
      Uppsala University, Sweden
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Error analysis of Lagrange interpolation on tetrahedrons2016

    • Author(s)
      小林健太, 土屋卓也
    • Organizer
      日本数学会2016年度秋季総合分科会
    • Place of Presentation
      関西大学千里山キャンパス(大阪府吹田市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] 重調和方程式の近似解に対する構成的誤差評価2016

    • Author(s)
      渡部善隆, 木下武彦, 中尾充宏
    • Organizer
      日本数学会2016年度秋季総合分科会
    • Place of Presentation
      関西大学千里山キャンパス(大阪府吹田市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] 重調和方程式の近似解に対する構成的誤差評価2016

    • Author(s)
      渡部善隆, 木下武彦, 中尾充宏
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] Stokes微分作用素の厳密な固有値評価について2016

    • Author(s)
      劉雪峰
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] Error analysis of Lagrange interpolation on tetrahedrons2016

    • Author(s)
      小林健太, 土屋卓也
    • Organizer
      日本応用数理学会2016年度年会
    • Place of Presentation
      北九州国際会議場(福岡県北九州市)
    • Related Report
      2016 Annual Research Report
  • [Presentation] Computable estimates of the evolution operator based on the operator theory2016

    • Author(s)
      Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, and Shin'ichi Oishi
    • Organizer
      Czech-Japanese-Polish Seminar in Applied Mathematics 2016 (CJPS 2016)
    • Place of Presentation
      Krakow, Polland
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Verified High-precision Eigenvalue Bounds for Partial Differential Operators2016

    • Author(s)
      Xuefeng Liu
    • Organizer
      5th European Seminar on Computing (ESCO 2016)
    • Place of Presentation
      Pilsen, Czech Republic
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Verified Computations for Solutions to Nonlinear Heat Equations Based on Fractional Powers of a Positive Operator and the Evolution Operator2016

    • Author(s)
      Akitoshi Takayasu, Makoto Mizuguchi, Takayuki Kubo, and Shin'ichi Oishi
    • Organizer
      5th European Seminar on Computing (ESCO 2016)
    • Place of Presentation
      Pilsen, Czech Republic
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The circumradius condition and its application2016

    • Author(s)
      Kenta Kobayashi
    • Organizer
      Numerical Computations: Theory and Algorithms (NUMTA2016)
    • Place of Presentation
      Club Med Resort "Napitia", Calabria, Italy
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A framework of high-precision verified eigenvalue bounds for self-adjoint differential operators2016

    • Author(s)
      Xuefeng Liu
    • Organizer
      The Mathematics of Finite Elements and Applications 2016 (MAFELAB 2016)
    • Place of Presentation
      Brunel University, England
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 四面体上のLagrange補間の誤差評価について2016

    • Author(s)
      小林健太, 土屋卓也
    • Organizer
      第21回計算工学講演会
    • Place of Presentation
      朱鷺メッセ:新潟コンベンションセンター(新潟県新潟市)
    • Related Report
      2016 Annual Research Report
  • [Book] Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations2019

    • Author(s)
      Mitsuhiro T. Nakao, Michael Plum, and Yoshitaka Watanabe
    • Total Pages
      467
    • Publisher
      Springer Singapore
    • ISBN
      9789811376696
    • Related Report
      2019 Annual Research Report

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Published: 2016-04-21   Modified: 2021-02-19  

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