新たな段階に入った有限要素法基盤の精度保証付き数値計算の進展

• Project/Area Number: 20H01820
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Hitotsubashi University
• Principal Investigator: 小林 健太 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 大阪大学, 数理・データ科学教育研究センター, 招へい研究員 (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 東京女子大学, 現代教養学部, 教授 (50571220) ; 高安 亮紀 筑波大学, システム情報系, 准教授 (60707743)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Project Status: Completed (Fiscal Year 2023)
• Budget Amount: ¥17,550,000 (Direct Cost: ¥13,500,000、Indirect Cost: ¥4,050,000); Fiscal Year 2023: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2022: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2021: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2020: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
• Keywords: 有限要素法 / 補間誤差解析 / 精度保証付き数値計算 / 非線形偏微分方程式 / 不連続ガレルキン法 / 逆作用素ノルム / Navier-Stokes方程式 / 計算機援用証明 / 誤差評価 / 制度保証付き数値計算

Outline of Research at the Start

本研究課題においては、近年の計算機の性能の向上と、有限要素法および精度保証付き数値計算に関してこれまで蓄積された知見を元に、空間3次元の非線形偏微分方程式に対する精度保証付き数値計算を飛躍的に進展させたいと考えています。この目的を達成するため、まずは3次元問題に精度保証付き数値計算を適用するための基盤整備、すなわち3次元有限要素法の誤差解析および効率的な精度保証手法の構築を行い、次いで、流体方程式など、数学的に重要な非線形偏微分方程式に対する精度保証の応用を実現します。

Outline of Annual Research Achievements

小林健太（研究代表者）と土屋卓也（分担者）は、2022年度に引き続き、有限要素法の誤差解析において重要となる有限要素上の補間誤差解析の精密化について研究を行った。2022年度までの研究で、小林と土屋は、三角形要素上および四面体要素上の補間誤差解析において、新たな幾何学的な量を導入することにより、２次元および３次元のケースを統合的に扱うことのできる一般理論を構築したが、2023年度においては、その幾何学的な量が、それ以前に四面体要素上の誤差評価のために導入した幾何学的な量である射影外接半径と同値かどうか研究を行った。この件については理論的な結果は得られなかったが、数値的には肯定的な結果が得られた。また小林と土屋は、補間誤差が悪くても、有限要素解の誤差が悪くならないような例について研究を行い、適当な条件下で、補間誤差が大きくなるような要素が存在しても、有限要素解の精度が悪くならないことを示した。
渡部善隆（分担者）は、2022年度に引き続き、線形化逆作用素の評価の効率化について研究を行い、楕円型方程式の精度保証付き数値計算の効率を向上させた。また、いくつかの個別の方程式に対しても精度保証付き数値計算に取り組んだ。具体的には、非線形波動方程式の自己相似爆発解に対する精度保証付き数値計算、および、Proudman-Johnson方程式の単峰性解の存在検証に成功した。
劉雪峰（分担者）は、楕円型方程式の局所誤差解析や、固有関数の誤差評価について研究を行い、精度保証付き数値計算を用いた検証に成功した。
高安亮紀（分担者）は、爆発解を持つ放物型方程式の精度保証付き数値計算の効率化を行った。また、エルミート固有値問題への精度保証付き数値計算手法の開発にも成功した。

Research Progress Status

令和5年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和5年度が最終年度であるため、記入しない。

Research Products

• [Journal Article] Correction to: General theory of interpolation error estimates on anisotropic meshes (2023)
  • Author(s): Ishizaka Hiroki、Kobayashi Kenta、Tsuchiya Takuya
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 40 Pages: 1355～1356
  • DOI: 10.1007/s13160-023-00582-x
  • Peer Reviewed / Open Access
• [Journal Article] Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error analysis (2023)
  • Author(s): Endo Ryoki、Liu Xuefeng
  • Journal Title: Journal of Differential Equations Volume: 376 Pages: 750～772
  • DOI: 10.1016/j.jde.2023.09.016
  • Peer Reviewed
• [Journal Article] Projection-based guaranteed L2 error bounds for finite element approximations of Laplace eigenfunctions (2023)
  • Author(s): Liu Xuefeng、Vejchodsk Tom
  • Journal Title: Journal of Computational and Applied Mathematics Volume: 429 Pages: 115164～115164
  • DOI: 10.1016/j.cam.2023.115164
  • Peer Reviewed
• [Journal Article] Guaranteed local error estimation for finite element solutions of boundary value problems (2023)
  • Author(s): Nakano Taiga、Liu Xuefeng
  • Journal Title: Journal of Computational and Applied Mathematics Volume: 425 Pages: 115061～115061
  • DOI: 10.1016/j.cam.2023.115061
  • Peer Reviewed / Open Access
• [Journal Article] Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems (2023)
  • Author(s): Imakura Akira、Morikuni Keiichi、Takayasu Akitoshi
  • Journal Title: Journal of Computational and Applied Mathematics Volume: 424 Pages: 114994～114994
  • DOI: 10.1016/j.cam.2022.114994
  • Peer Reviewed / Open Access
• [Journal Article] Inclusion method of optimal constant with quadratic convergence for H^0_1-projection error estimates and its applications (2023)
  • Author(s): Kinoshita Takehiko、Watanabe Yoshitaka、Yamamoto Nobito、Nakao Mitsuhiro T.
  • Journal Title: Journal of Computational and Applied Mathematics Volume: 417 Pages: 114521～114521
  • DOI: 10.1016/j.cam.2022.114521
  • Peer Reviewed / Open Access
• [Journal Article] Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces (2023)
  • Author(s): Watanabe Yoshitaka、Kinoshita Takehiko、Nakao Mitsuhiro T.
  • Journal Title: Journal of Scientific Computing Volume: 94 Pages: -
  • DOI: 10.1007/s10915-023-02097-6
  • Peer Reviewed / Open Access
• [Journal Article] Guaranteed Lower Eigenvalue Bounds for Steklov Operators Using Conforming Finite Element Methods (2023)
  • Author(s): Nakano Taiga、Li Qin、Yue Meiling、Liu Xuefeng
  • Journal Title: Computational Methods in Applied Mathematics Volume: 24 Pages: 495～510
  • DOI: 10.1515/cmam-2022-0218
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Saddle-Type Blow-Up Solutions with Computer-Assisted Proofs: Validation and Extraction of Global Nature (2023)
  • Author(s): Lessard Jean-Philippe、Matsue Kaname、Takayasu Akitoshi
  • Journal Title: Journal of Nonlinear Science Volume: 33 Pages: -
  • DOI: 10.1007/s00332-023-09900-6
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Anisotropic interpolation error estimates using a new geometric parameter (2022)
  • Author(s): Ishizaka Hiroki、Kobayashi Kenta、Tsuchiya Takuya
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 40 Pages: 475～512
  • DOI: 10.1007/s13160-022-00535-w
  • Peer Reviewed / Open Access
• [Journal Article] Improvement of infinity norm estimations related to computer-assisted proofs of the Kolmogorov problem (2022)
  • Author(s): Kobayashi Kenta、Watanabe Yoshitaka
  • Journal Title: JSIAM Letters Volume: 14 Pages: 92～95
  • DOI: 10.14495/jsiaml.14.92
  • Peer Reviewed / Open Access
• [Journal Article] On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators (2022)
  • Author(s): Kinoshita Takehiko、Watanabe Yoshitaka、T. Nakao Mitsuhiro
  • Journal Title: Acta Cybernetica Volume: 26 Pages: 71～82
  • DOI: 10.14232/actacyb.294906
  • Peer Reviewed / Open Access
• [Journal Article] Fully computable a posteriori error bounds for eigenfunctions (2022)
  • Author(s): Liu Xuefeng、Vejchodsky Tomas
  • Journal Title: Numerische Mathematik Volume: 152 Pages: 183～221
  • DOI: 10.1007/s00211-022-01304-0
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Error-constant estimation under the maximum norm for linear Lagrange interpolation (2022)
  • Author(s): Galindo Shirley Mae、Ike Koichiro、Liu Xuefeng
  • Journal Title: Journal of Inequalities and Applications Volume: 109 Pages: -
  • DOI: 10.1186/s13660-022-02841-w
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains (2022)
  • Author(s): Liu Xuefeng、Nakao Mitsuhiro T.、Oishi Shin’ichi
  • Journal Title: Communications in Nonlinear Science and Numerical Simulation Volume: 108 Pages: 106223～106223
  • DOI: 10.1016/j.cnsns.2021.106223
  • Peer Reviewed
• [Journal Article] Rigorous numerics for nonlinear heat equations in the complex plane of time (2022)
  • Author(s): Takayasu Akitoshi、Lessard Jean-Philippe、Jaquette Jonathan、Okamoto Hisashi
  • Journal Title: Numerische Mathematik Volume: 151 Pages: 693～750
  • DOI: 10.1007/s00211-022-01291-2
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity (2022)
  • Author(s): Jaquette Jonathan、Lessard Jean-Philippe、Takayasu Akitoshi
  • Journal Title: Communications in Nonlinear Science and Numerical Simulation Volume: 107 Pages: 106188～106188
  • DOI: 10.1016/j.cnsns.2021.106188
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Lectures on the error analysis of interpolation on simplicial triangulations without the shape regularity assumption and its applications to finite element methods. part 1: Lagrange interpolation on triangles (2022)
  • Author(s): 小林健太, 土屋卓也
  • Journal Title: 愛媛大学理学部紀要 Volume: 24 Pages: 9～42
  • Peer Reviewed
• [Journal Article] Robust Algebraic Curve Intersections with Tolerance Control (2022)
  • Author(s): Shao Wenbing、Chen Falai、Liu Xuefeng
  • Journal Title: Computer-Aided Design Volume: 147 Pages: 103236～103236
  • DOI: 10.1016/j.cad.2022.103236
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Global dynamics in nonconservative nonlinear Schr?dinger equations (2022)
  • Author(s): Jaquette Jonathan、Lessard Jean-Philippe、Takayasu Akitoshi
  • Journal Title: Advances in Mathematics Volume: 398 Pages: 108234～108234
  • DOI: 10.1016/j.aim.2022.108234
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A new geometric condition equivalent to the maximum angle condition for tetrahedrons (2021)
  • Author(s): Ishizaka Hiroki、Kobayashi Kenta、Suzuki Ryo、Tsuchiya Takuya
  • Journal Title: Computers & Mathematics with Applications Volume: 99 Pages: 323～328
  • DOI: 10.1016/j.camwa.2021.08.017
  • Peer Reviewed
• [Journal Article] A robust discontinuous Galerkin scheme on anisotropic meshes (2021)
  • Author(s): Kashiwabara Takahito、Tsuchiya Takuya
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 38 Pages: 1001～1022
  • DOI: 10.1007/s13160-021-00474-y
  • Peer Reviewed
• [Journal Article] Computer-assisted proofs of the existence of a symmetry-breaking bifurcation point for the Kolmogorov problem (2021)
  • Author(s): Cai Shuting、Watanabe Yoshitaka
  • Journal Title: Journal of Computational and Applied Mathematics Volume: 395 Pages: 113603～113603
  • DOI: 10.1016/j.cam.2021.113603
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Crouzeix?Raviart and Raviart?Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition (2021)
  • Author(s): Ishizaka Hiroki、Kobayashi Kenta、Tsuchiya Takuya
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 38 Pages: 645～675
  • DOI: 10.1007/s13160-020-00455-7
  • Peer Reviewed
• [Journal Article] Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations (2021)
  • Author(s): Liu Xuefeng、Nakao Mitsuhiro T.、You Chun’guang、Oishi Shin’ichi
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 38 Pages: 545～559
  • DOI: 10.1007/s13160-020-00449-5
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] General theory of interpolation error estimates on anisotropic meshes (2020)
  • Author(s): Ishizaka Hiroki、Kobayashi Kenta、Tsuchiya Takuya
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 38 Pages: 163～191
  • DOI: 10.1007/s13160-020-00433-z
  • Peer Reviewed
• [Journal Article] Numerical validation of blow-up solutions with quasi-homogeneous compactifications (2020)
  • Author(s): Matsue Kaname、Takayasu Akitoshi
  • Journal Title: Numerische Mathematik Volume: 145 Pages: 605～654
  • DOI: 10.1007/s00211-020-01125-z
  • Peer Reviewed
• [Journal Article] A computer-assisted proof for nonlinear heat equations in the complex plane of time (2020)
  • Author(s): Takayasu Akitoshi
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B82 Pages: 47～66
  • Peer Reviewed
• [Presentation] Error estimation for the FEM solution with a few bad elements (2024)
  • Author(s): Kenta Kobayashi
  • Organizer: Seventh Chilean Workshop on Numerical Analysis of Partial Differential Equations (WONAPDE 2024)
  • Int'l Joint Research
• [Presentation] 悪い要素を含む有限要素解の誤差解析 (2024)
  • Author(s): 小林健太
  • Organizer: 北陸応用数理研究会2024
  • Invited
• [Presentation] Some computer-assisted proofs for nonlinear differential equations involved with self-similar blowup in wave equations (2024)
  • Author(s): Yoshitaka Watanabe
  • Organizer: Nonlinear Analysis, Spectral theory and PDEs, Workshop in Honor of Prof. Dr. Michael Plum
  • Int'l Joint Research / Invited
• [Presentation] 近似楕円型線形作用素のノルムに関する収束性評価の改良 (2024)
  • Author(s): 木下武彦, 渡部善隆, 中尾充宏
  • Organizer: 日本応用数理学会第20回(2024年)研究部会連合発表会
• [Presentation] 線形作用素の近似逆作用素ノルムに対する精度保証付き数値計算 (2024)
  • Author(s): 寺尾剛史, 渡部善隆, 尾崎克久
  • Organizer: 日本応用数理学会第20回(2024年)研究部会連合発表会
• [Presentation] 実2×2行列の2ノルムと近似逆作用素ノルムの収束オーダーの改善について (2024)
  • Author(s): 木下武彦, 渡部善隆, 中尾充宏
  • Organizer: 日本数学会2024年年会
• [Presentation] 無限次元線形作用素の近似逆作用素ノルムに対する精度保証付き特異値計算 (2024)
  • Author(s): 寺尾剛史, 渡部善隆, 尾崎克久
  • Organizer: 日本数学会2024年年会
• [Presentation] A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory (2024)
  • Author(s): Akitoshi Takayasu
  • Organizer: Workshop of Computational Science and Information Engineering 2024 (SCIE2024)
• [Presentation] Error estimation for the FEM solution with a few bad elements (2023)
  • Author(s): Kenta Kobayashi
  • Organizer: International Congress on Industrial and Applied Mathematics (ICIAM2023)
  • Int'l Joint Research
• [Presentation] 悪い形の要素がそれほど多くないときの有限要素法の誤差評価 (2023)
  • Author(s): 小林健太
  • Organizer: 隠岐島応用数学研究会
• [Presentation] A computer-assisted proof for a nonlinear differential equation involved with self-similar blowup in wave equations (2023)
  • Author(s): Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Birgit Schorkhuber, and Mitsuhiro T. Nakao
  • Organizer: International Congress on Industrial and Applied Mathematics (ICIAM2023)
  • Int'l Joint Research
• [Presentation] 精度保証付き数値計算によるProudman-Johnson方程式の単峰性解の存在検証 (2023)
  • Author(s): 渡部善隆, 宮路智行
  • Organizer: 日本数学会2023年度秋季総合分科会
• [Presentation] 非線形波動方程式の自己相似爆発解に対する精度保証付き数値計算 (2023)
  • Author(s): 渡部善隆
  • Organizer: RIMS共同研究(公開型)「新時代における高性能科学技術計算法の探究」
  • Invited
• [Presentation] Recent Results of Rigorous Numerical Integration for Higher Spatial Dimensional PDEs (2023)
  • Author(s): Akitoshi Takayasu, Gabriel Duchesne, Jean-Philippe Lessard
  • Organizer: SIAM Conference on Applications of Dynamical Systems
  • Int'l Joint Research
• [Presentation] Rigorous forward numerical integration of general evolutionary partial differential equations based on semigroup theory (2023)
  • Author(s): Akitoshi Takayasu, Gabriel Duchesne, Jean-Philippe Lessard
  • Organizer: IUTAM Symposium on Nonlinear dynamics for design of mechanical systems across different length/time scales (IUTAM 2023)
  • Int'l Joint Research
• [Presentation] Rigorous numerics for finding the monodromy of Picard-Fuchs differential equations for a family of K3 toric hypersurfaces (2023)
  • Author(s): Akitoshi Takayasu, Toshimasa Ishige
  • Organizer: International Congress on Industrial and Applied Mathematics (ICIAM2023)
  • Int'l Joint Research
• [Presentation] Global Dynamics and Blowup in Some Quadratic PDEs (2023)
  • Author(s): Jonathan Jaquette, Jean-Philippe Lessard, Akitoshi Takayasu
  • Organizer: International Congress on Industrial and Applied Mathematics (ICIAM2023)
  • Int'l Joint Research
• [Presentation] Approximation of minimal surfaces by the method of fundamental solution (2023)
  • Author(s): 土屋卓也
  • Organizer: 環瀬戸内ワークショップ
• [Presentation] 楕円型線形作用素に対する近似逆作用素ノルムの収束性評価 (2023)
  • Author(s): 木下武彦, 渡部善隆, 中尾充宏
  • Organizer: 日本応用数理学会2023年研究部会連合発表会
• [Presentation] 2階楕円型線形作用素に対する近似逆作用素ノルムの収束オーダー評価 (2023)
  • Author(s): 木下武彦, 渡部善隆, 中尾充宏
  • Organizer: 日本数学会2023年年会
• [Presentation] Rigorous integrator for higher spatial dimensional PDEs (2022)
  • Author(s): Takayasu, Akitoshi, Lessard, Jean-Philippe
  • Organizer: SIAM Conference on Nonlinear Waves and Coherent Structures (NWCS22)
  • Int'l Joint Research
• [Presentation] A general approach for rigorously integrating PDEs using semigroup theory (2022)
  • Author(s): Takayasu, Akitoshi
  • Organizer: CRM Applied Mathematics Seminars
  • Int'l Joint Research / Invited
• [Presentation] 異方的なメッシュ上でも頑健な不連続Galerkin法について (2022)
  • Author(s): 土屋卓也
  • Organizer: 第27回計算工学講演会
• [Presentation] Proudman-Johnson方程式の定常解に対する精度保証付き数値計算 ～Miyaji-Okamoto定理の別証～ (2022)
  • Author(s): 渡部善隆
  • Organizer: 日本応用数理学会2022年度年会
• [Presentation] 精度保証付き数値計算によるProudman Johnson 方程式の定常解の存在別証 (2022)
  • Author(s): 渡部善隆
  • Organizer: 日本数学会2022年度秋季総合分科会
• [Presentation] 半群理論に基づく一般的な時間発展方程式に対する厳密な数値求積法 (2022)
  • Author(s): 高安亮紀
  • Organizer: 2022年度応用数学合同研究集会
• [Presentation] 常微分方程式の爆発解の漸近展開と無限遠ダイナミクスの対応 (2022)
  • Author(s): 松江要, 落合啓之, 小谷久寿, 高安亮紀
  • Organizer: 2022年度応用数学合同研究集会
• [Presentation] 遅延Duffing方程式の結合系の完全同期解に対する精度保証付き数値計算 (2022)
  • Author(s): 高橋和暉, 高安亮紀
  • Organizer: RIMS 共同研究（公開型）時間遅れ系と数理科学：理論と応用の新たな展開に向けて
  • Invited
• [Presentation] 時間発展方程式に対する厳密な数値求積法の最近の進展 (2022)
  • Author(s): 高橋和暉, 高安亮紀
  • Organizer: RIMS 共同研究（公開型）数値解析が拓く次世代情報社会～エッジから富岳まで～
  • Invited
• [Presentation] Chebyshev補間の最大値最小値の精度保証付き数値計算 (2022)
  • Author(s): 近藤慎佑, 高安亮紀
  • Organizer: 日本応用数理学会2022年度年会
• [Presentation] 遅延Duffing方程式の結合系に対する同期解の精度保証付き数値計算 (2022)
  • Author(s): 高橋和暉, 高安亮紀
  • Organizer: 日本応用数理学会2022年度年会
• [Presentation] 2階楕円型境界値問題から導かれる近似作用素ノルムの収束性 (2022)
  • Author(s): 渡部善隆, 木下武彦, 中尾充宏
  • Organizer: 日本応用数理学会2022年研究部会連合発表会
• [Presentation] A computer-assisted proof toward the critical Reynolds number for the Orr-Sommerfeld problem (2022)
  • Author(s): Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Takehiko Kinoshita, Mitsuhiro T. Nakao
  • Organizer: International Workshop on Reliable Computing and Computer-Assisted Proofs (ReCAP 2022)
  • Int'l Joint Research
• [Presentation] OrrSommerfeld方程式の臨界Reynolds数に対する計算機援用証明 (2022)
  • Author(s): 渡部善隆、長藤かおり、Michael Plum、木下武彦、中尾充宏
  • Organizer: 日本数学会2022年年会
• [Presentation] Chebyshev interpolation for rigorous integrator of differential equations (2022)
  • Author(s): Akitoshi Takayasu
  • Organizer: International Workshop on Reliable Computing and Computer-Assisted Proofs (ReCAP 2022)
  • Int'l Joint Research
• [Presentation] 異方的なメッシュ上での有限要素誤差解析について (2021)
  • Author(s): 土屋卓也
  • Organizer: 東京大学数値解析セミナー
  • Invited
• [Presentation] 四面体の最大角条件と同値な幾何学的条件について (2021)
  • Author(s): 土屋卓也
  • Organizer: 第26回計算工学講演会
• [Presentation] 定常Kolmogorov問題の対称性破壊分岐点に対する精度保証付き数値計算 (2021)
  • Author(s): 渡部善隆
  • Organizer: 日本応用数理学会2021年度年会
• [Presentation] On some convergence properties for finite element approximations to the inverse of linear elliptic operators (2021)
  • Author(s): Takehiko Kinoshita, Yoshitaka Watanabe, and Mitsuhiro T. Nakao
  • Organizer: 19th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2020)
  • Int'l Joint Research
• [Presentation] Kolmogorov問題の対称性破壊分岐点に対する計算機援用証明 (2021)
  • Author(s): 渡部善隆
  • Organizer: 日本数学会2021年度秋季総合分科会
• [Presentation] 非線形微分方程式に対する精度保証付き数値計算 (2021)
  • Author(s): 渡部善隆
  • Organizer: CREST「現代の数理科学と連携するモデリング手法の構築」 成果報告公開シンポジウム
• [Presentation] 非線形熱方程式の複素時間領域における解の精度保証付き数値計算 (2021)
  • Author(s): 高安亮紀
  • Organizer: 東京大学数値解析セミナー
  • Invited
• [Presentation] Global dynamics in nonconservative nonlinear Schrodinger equations (2021)
  • Author(s): 高安亮紀
  • Organizer: 京都大学NLPDEセミナー
• [Presentation] Rigorous integrator for dissipative PDEs using the Chebyshev-Fourier spectral method (2021)
  • Author(s): Akitoshi Takayasu, Jean-Philippe Lessard
  • Organizer: Conference on Applications of Dynamical Systems (DS21)
  • Int'l Joint Research
• [Presentation] Swift-Hohenberg方程式の厳密な数値求積法 (2021)
  • Author(s): 高安亮紀
  • Organizer: 日本応用数理学会2021年度年会
• [Presentation] A rigorous forward integration method for time-dependent PDEs (2021)
  • Author(s): Akitoshi Takayasu, Jean-Philippe Lessard
  • Organizer: 19th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2020)
  • Int'l Joint Research
• [Presentation] ある連立遅延微分方程式系の星形周期解ー数値的根拠と精度保証ー (2021)
  • Author(s): 高安亮紀
  • Organizer: RIMS共同研究（公開型）時間遅れ系と数理科学：理論と応用の新たな展開に向けて
  • Invited
• [Presentation] Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity (2021)
  • Author(s): 高安亮紀, Jonathan Jaquette, Jean-Philippe Lessard
  • Organizer: 2021年度応用数学合同研究集会
• [Presentation] Kolmogorov問題に対する計算機援用証明における最大値ノルム評価とその応用 (2021)
  • Author(s): 小林健太, 渡部善隆
  • Organizer: 日本応用数理学会2021年研究部会連合発表会
• [Presentation] A robust discontinuous Galerkin scheme on anisotropic meshes (2021)
  • Author(s): 土屋卓也
  • Organizer: IAS conference Industrial and Applied Mathematics
  • Int'l Joint Research / Invited
• [Presentation] Global dynamics in a quadratic nonlinear Schrodinger equation (2021)
  • Author(s): Jonathan Jaquette, Jean-Philippe Lessard, 高安亮紀
  • Organizer: 日本数学会2021年度年会
• [Presentation] 遅延微分方程式に対する精度保証付き数値計算ー現状と課題ー (2021)
  • Author(s): 高安亮紀
  • Organizer: 第2回 時間遅れと数理セミナー
  • Invited
• [Presentation] Global existence and heteloclinics/homoclinics to a quadratic nonlinear Schrodinger equation (2021)
  • Author(s): Akitoshi Takayasu
  • Organizer: Czech-Japanese Seminar in Applied Mathematics
  • Int'l Joint Research
• [Presentation] 重調和方程式の近似解に対する構成的誤差評価の改良 (2021)
  • Author(s): 渡部善隆, 木下武彦, 中尾充宏
  • Organizer: 日本数学会2021年年会
• [Presentation] 異方的三角形分割上でもロバストな不連続Galerkinスキーム (2020)
  • Author(s): 土屋卓也
  • Organizer: 日本数学会2020年度秋季総合分科会
• [Presentation] 異方的三角形分割上でもロバストな不連続Galerkinスキーム (2020)
  • Author(s): 土屋卓也
  • Organizer: 日本応用数理学会2020年度年会
• [Presentation] Computer-assisted proofs of heteloclinic orbits to a quadratic nonlinear Schrodinger equation (2020)
  • Author(s): 高安亮紀, Jonathan Jaquette, Jean-Philippe Lessard
  • Organizer: 2020年度応用数学合同研究集会
• [Presentation] Global dynamics in a quadratic nonlinear Schrodinger equation (2020)
  • Author(s): 高安亮紀
  • Organizer: 第4回 精度保証付き数値計算の実問題への応用研究集会 (NVR 2020)
  • Invited
• [Presentation] Computer-assisted proofs for finding the monodromy of hypergeometric differential equations (2020)
  • Author(s): Akitoshi Takayasu
  • Organizer: 16th Seminar Series of CRM CAMP in Nonlinear Analysis
  • Int'l Joint Research / Invited
• [Presentation] Homoclinics and global existence of solutions to a quadratic nonlinear Schrodinger equation (2020)
  • Author(s): 高安亮紀, Jonathan Jaquette
  • Organizer: 日本数学会2020年度秋季総合分科会
• [Presentation] 非線形シュレディンガー方程式の厳密な数値求積法 (2020)
  • Author(s): 高安亮紀
  • Organizer: 日本応用数理学会2020年度年会
• [Presentation] Hilbert空間における線形作用素に対する可逆性検証の効率化とその応用 (2020)
  • Author(s): 渡部善隆, 木下武彦, 中尾充宏
  • Organizer: 日本数学会2020年度秋季総合分科会
• [Presentation] Hilbert空間における線形作用素に対する可逆性検証の効率化 (2020)
  • Author(s): 渡部善隆, 木下武彦, 中尾充宏
  • Organizer: 日本応用数理学会2020年度年会