A posteriori analysis of the finite element approximation for nonlinear parabolic problems

• Project/Area Number: 18740046
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: The University of Tokyo (2007-2008); University of Toyama (2006)
• Principal Investigator: NORIKAZU Saito The University of Tokyo, 大学院数理科学研究科, 准教授 (00334706)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000); Fiscal Year 2006: ¥1,700,000 (Direct Cost: ¥1,700,000)
• Keywords: 有限要素法 / 誤差解析 / 非線形放物型偏微分方程式 / 補間空間 / 事後解析 / 放物型問題 / 非線形問題

Research Abstract

非線形放物型偏微分方程式の有限要素法による近似解法を考え、その事前・事後誤差評価を行い、数値解から解の定量的な情報を引き出すことに成功した。具体的な対象としては、差細胞性粘菌の凝集現象を記述するKeller-Segel系や、解の爆発のモデル問題として有名なFujita方程式を扱った。

Research Products

• [Journal Article] Flux-free finite element method with Lagrange multipliers for two-fluid flows (2007)
  • Author(s): K. Ohmori and N. Saito
  • Journal Title: Journal of Scientific Computing Vol. 32, No. 2 Pages: 147-173
• [Journal Article] Conservative upwind finite element method for a simplified Keller-Segel system modelling chemotaxis (2007)
  • Author(s): N. Saito
  • Journal Title: IMA Journal of Numerical Analysis Vol. 27, No. 2 Pages: 332-365
• [Journal Article] On the convergence of finite element solutions to the interface problem for the Stokes system (2007)
  • Author(s): K. Ohmori and N. Saito
  • Journal Title: Journal of Computational and Applied Mathematics Vol. 198, No. 1 Pages: 116-128
• [Journal Article] On interpolation spaces in a polygon (2007)
  • Author(s): N. Saito
  • Journal Title: 富山大学人間発達科学部紀要 第2巻, 第1号 Pages: 7-12
  • NAID: 120002227005
• [Journal Article] 腫瘍の浸潤を記述する数理モデルへの差分法 (2007)
  • Author(s): 林賢治、齊藤宣一
  • Journal Title: 日本応用数理学会論文誌 第17巻、第3号 Pages: 331-345
• [Journal Article] Flux-free finite elemen method with Lagrange multipliers for two-fluid flows (2007)
  • Author(s): K. Ohmori and N. Saito
  • Journal Title: Journal of Scientific Computing 32 Pages: 147-173
  • Peer Reviewed
• [Journal Article] Conservative upwind finite element method for a simplified Keller-Segel system modelling chemotaxis (2007)
  • Author(s): N. Saito
  • Journal Title: IMA Journal of Numerical Analysis 27 Pages: 332-365
  • Peer Reviewed
• [Journal Article] On interpolation spaces in a polygon (2007)
  • Author(s): N. Saito
  • Journal Title: 富山大学人間発達科学部紀要 7 Pages: 7-12
  • NAID: 120002227005
  • Peer Reviewed
• [Journal Article] An interpretation of the Scharfetter-Gummel finite difference scheme (2007)
  • Author(s): Norikazu Saito
  • Journal Title: Proceedings of the Japan Academy, Ser. A 82(10) Pages: 187-191
  • NAID: 40015216623
• [Journal Article] On the convergence of finite element solutions to the interface problem for the Stokes system (2007)
  • Author(s): Katsushi Ohmori, Norikazu Saito
  • Journal Title: Journal of Computational and Applied Mathematics 198(1) Pages: 116-128
• [Journal Article] An interpretation of the Scharfetter-Gummel finite difference scheme (2006)
  • Author(s): N. Saito
  • Journal Title: Proceedings of the Japan Academy, Ser. A Vol. 82, No. 10 Pages: 187-191
  • NAID: 40015216623
• [Journal Article] Mass conservative finite element method with Lagrange multipliers for two-fluid flows (2006)
  • Author(s): K. Ohmori and N. Saito
  • Journal Title: Proceedings of the Seventh China-Japan Joint Seminar on Numerical Mathematics (Z. Shi and H. Okamoto eds.) Science Press, Beijing, China Pages: 107-119
• [Journal Article] Field variation and mathematics of blowup (2006)
  • Author(s): N. Saito and T. Suzuki
  • Journal Title: 京都大学数理解析研究所講究録 Vol. 1505 Pages: 106-120
• [Journal Article] Mathematical models of tumour angiogenesis and simulations (2006)
  • Author(s): A. Kubo, N. Saito, T. Suzuki and H. Hoshino
  • Journal Title: 京都大学数理解析研究所講究録 Vol. 1499 Pages: 135-146
• [Journal Article] Shape-dependence of convergence rates in DDM, Domain Decomposition Methods: Theory and Applications GAKUTO International Series (2006)
  • Author(s): H. Fujita and N. Saito
  • Journal Title: GAKUTO International Series Mathematical Sciences and Applications, Gakkotosho Vol. 25 Pages: 241-271
• [Journal Article] On a duality in W^{1,p} defined on nonsmooth domains (2006)
  • Author(s): N. Saito
  • Journal Title: 富山大学教育学部紀要 No. 60 Pages: 107-115
  • NAID: 110004661941
• [Presentation] 走化性Keller-Segel系の有限要素近似 (2007)
  • Organizer: 日本数学会(応用数学分科会)特別講演
  • Place of Presentation: 埼玉大学理学部