Numerical verification of solutions for parabolic problems based on the finite element method

• Project/Area Number: 18K03440
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Nakamura Gakuen University Junior College
• Principal Investigator: Hashimoto Kouji 中村学園大学短期大学部, 幼児保育学科, 准教授 (40455093)
• Project Period (FY): 2018-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2018: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 数値的検証法 / 発展方程式 / 有限要素法 / 構成的誤差評価

Outline of Final Research Achievements

Using the full-descrete finite element scheme which is satisfied the numerical stability, we presented the numerical verification method for solutions of nonlinear parabolic problems.

Academic Significance and Societal Importance of the Research Achievements

これまでに提案されていなかった一般的な数値計算法である有限要素法を基盤とする発展方程式の解軌道に対する数値的検証法の構築により、発展方程式に対する新たな数値解法を提案することができた。

Research Products

• [Journal Article] Constructive error analysis of a fulldiscrete finite element method for the heat equations (2019)
  • Author(s): Hashimoto, K., Kimura, T., Minamoto, T., Nakao, M.T.
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 36 Issue: 3 Pages: 777-790
  • DOI: 10.1007/s13160-019-00362-6
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Constructive error analysis of a full-discrete finite element method for the heat equation (2019)
  • Author(s): Kouji Hashimoto , Takuma Kimura , Teruya Minamoto , Mitsuhiro Nakao
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: 印刷中
  • NAID: 210000186122
  • Peer Reviewed
• [Presentation] 非線形放物型方程式の解の検証における初期値分離型評価の包含効果抑制について (2020)
  • Author(s): 木下武彦, 橋本弘治, 中尾充宏
  • Organizer: 日本数学会2020年度秋季総合分科会
• [Presentation] 藤田型方程式の解の爆発時間に対する計算機を用いた数値的包含方法について (2020)
  • Author(s): 水口信, 関根晃太, 橋本弘治, 中尾充宏, 大石進一
  • Organizer: 応用数学合同研究集会
• [Presentation] Constructive error analysis of a full-discrete finite element method for the heat equation (2019)
  • Author(s): Kouji Hashimoto
  • Organizer: The 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019)
  • Int'l Joint Research
• [Presentation] 非線形発展方程式の初期値問題に対する数値的検証法 (2019)
  • Author(s): 橋本弘治
  • Organizer: 第24回情報・統計科学シンポジウ
• [Presentation] 発展方程式の初期値問題に対する数値的検証法 (2018)
  • Author(s): 橋本弘治
  • 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)
  • Invited