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A new development of mathematical theory of Discontinuous Galerkin FEM

Research Project

Project/Area Number 15H03635
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

Saito Norikazu  東京大学, 大学院数理科学研究科, 教授 (00334706)

Co-Investigator(Kenkyū-buntansha) 松尾 宇泰  東京大学, 大学院情報理工学系研究科, 教授 (90293670)
小林 健太  一橋大学, 大学院経営管理研究科, 教授 (60432902)
村川 秀樹  九州大学, 数理学研究院, 助教 (40432116)
柏原 崇人  東京大学, 大学院数理科学研究科, 助教 (80771477)
Research Collaborator OIKAWA Issei  
Project Period (FY) 2015-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥16,770,000 (Direct Cost: ¥12,900,000、Indirect Cost: ¥3,870,000)
Fiscal Year 2018: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2016: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Keywords不連続Galerkin法 / 有限要素法 / 楕円型方程式 / 放物型方程式 / 非線形問題 / 誤差解析 / 構造保存型数値解法 / 発展方程式 / 数値解析 / 有限体積法 / 不連続ガレルキン法 / 楕円型界面問題
Outline of Final Research Achievements

This study project has succeeded in establishing the foundational theory of the discontinuous Galerkin finite element method (DG method) and the hybridized DG method (HDG method), which are extended versions combining the advantages of the finite element method (FEM) and the finite volume method (FVM) with a high-precision. This project aims to go beyond the negative position of making only the theory and leaving the application to engineers and to construct a mathematical theory that is required in real applications. Specifically, structural preservation (flux, positivity) methods and analytical theory (such as stability and convergence in practical sense) were constructed for nonstandard diffusion problems, degenerate diffusion problem and evolution problems appearing in various fields.

Academic Significance and Societal Importance of the Research Achievements

偏微分方程式の数値計算に基づくシミュレーションは,現代における最も強力な科学技術の一つであり,数学的な立場からの数値計算方法の研究(数値解析)は,これらの科学技術の屋台骨を支える基盤と言える.しかし,数学者と技術者では,研究の方向性が異なり,実際,経験に大きく依存した大規模計算によるスピード感ある研究に,数値解析の理論が追い付けてなかった.しかし,この溝を放置すれば,数学的方法における数学の不在に繋がり,発展は頭打ちとなるであろう.本研究は,数学理論のこの溝を埋めつつ,数値解析自体の更なる深化を実現した.

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Annual Research Report
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • Research Products

    (122 results)

All 2019 2018 2017 2016 2015

All Journal Article (29 results) (of which Int'l Joint Research: 11 results,  Peer Reviewed: 29 results,  Open Access: 4 results,  Acknowledgement Compliant: 7 results) Presentation (92 results) (of which Int'l Joint Research: 36 results,  Invited: 33 results) Funded Workshop (1 results)

  • [Journal Article] Stability and error estimates for the successive-projection technique with B-splines in time2019

    • Author(s)
      Y. Ueda and N. Saito
    • Journal Title

      J. Comput. Appl. Math.

      Volume: 358(1) Pages: 266-278

    • DOI

      10.1016/j.cam.2019.03.026

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The inf-sup condition and error estimates of the Nitsche method for evolutionary diffusion-advection-reaction equations2019

    • Author(s)
      Y. Ueda and N. Saito
    • Journal Title

      Jpn. J. Ind. Appl. Math.

      Volume: 36(1) Issue: 1 Pages: 209-238

    • DOI

      10.1007/s13160-018-0338-4

    • NAID

      210000180976

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exact solutions of nonlinear diffusion-convection-reaction equation: A Lie symmetry analysis approach2019

    • Author(s)
      M. Molati and H. Murakawa
    • Journal Title

      Commun. Nonlinear Sci. Numer. Simul.

      Volume: 67 Pages: 253-263

    • DOI

      10.1016/j.cnsns.2018.06.024

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Analysis of the immersed boundary method for a finite element Stokes problem2018

    • Author(s)
      N. Saito and Y. Sugitani
    • Journal Title

      Numer. Methods Partial Differential Equations

      Volume: 35(1) Issue: 1 Pages: 181-199

    • DOI

      10.1002/num.22296

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hybridized discontinuous Galerkin method for elliptic interface problems: error estimates under low regularity assumptions of solutions2018

    • Author(s)
      M. Miyashita and N. Saito
    • Journal Title

      J. Sci. Comput.

      Volume: 76(3) Issue: 3 Pages: 1657-1673

    • DOI

      10.1007/s10915-018-0678-x

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Extension of an error analysis of the randomized Kaczmarz method for inconsistent linear systems2018

    • Author(s)
      Yushi Morijiri, Kensuke Aishima, and Takayasu Matsuo
    • Journal Title

      JSIAM Letters

      Volume: 10 Issue: 0 Pages: 17-20

    • DOI

      10.14495/jsiaml.10.17

    • NAID

      130007404199

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] An efficient linear scheme to approximate nonlinear diffusion problems2018

    • Author(s)
      H. Murakawa
    • Journal Title

      Jpn. J. Ind. Appl. Math.

      Volume: 35(1) Issue: 1 Pages: 71-101

    • DOI

      10.1007/s13160-017-0279-3

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some Discrete Inequalities for Central-Difference Type Operators2017

    • Author(s)
      Hiroki Kojima, Takayasu Matsuo and Daisuke Furihata
    • Journal Title

      Mathematics of Computation

      Volume: 86 Issue: 306 Pages: 1719-1739

    • DOI

      10.1090/mcom/3154

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [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] A penalty method for the time-dependent Stokes problem with the slip boundary condition and its finite element approximation2017

    • Author(s)
      Zhou Guanyu、Kashiwabara Takahito、Oikawa Issei
    • Journal Title

      Applications of Mathematics

      Volume: 62 Issue: 4 Pages: 377-403

    • DOI

      10.21136/am.2017.0328-16

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strong time-periodic solutions to the 3D primitive equations subject to arbitrary large forces2017

    • Author(s)
      Galdi Giovanni P、Hieber Matthias、Kashiwabara Takahito
    • Journal Title

      Nonlinearity

      Volume: 30 Issue: 10 Pages: 3979-3992

    • DOI

      10.1088/1361-6544/aa8166

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] An efficient linear numerical scheme for the Stefan problem,the porous medium equation and nonlinear cross-diffusion systems2017

    • Author(s)
      M. Molati and H. Murakawa
    • Journal Title

      Proceedings of Equadiff 2017 Conference

      Volume: 1 Pages: 305-314

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Carbon-nanotube geometries as optimal configurations2017

    • Author(s)
      E. Mainini,H. Murakawa,P. Piovano and U. Stefanelli
    • Journal Title

      Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal

      Volume: 15(4) Issue: 4 Pages: 1448-1471

    • DOI

      10.1137/16m1087862

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Finite volume methods for a Keller-Segel system: discrete energy, error estimates and numerical blow-up analysis2017

    • Author(s)
      G. Zhou and N. Saito
    • Journal Title

      Numerische Mathematik

      Volume: 135 Issue: 1 Pages: 265-311

    • DOI

      10.1007/s00211-016-0793-2

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reelin transiently promotes N-cadherin-dependent neuronal adhesion during mouse cortical development2017

    • Author(s)
      Yuki Matsunaga, Mariko Noda, Hideki Murakawa, Kanehiro Hayashi, Arata Nagasaka, Seika Inoue, Takaki Miyata, Takashi Miura, Ken-ichiro Kubo, and Kazunori Nakajima
    • Journal Title

      Proc. Natl. Acad. Sci. U.S.A.

      Volume: 114 Issue: 8 Pages: 2048-2053

    • DOI

      10.1073/pnas.1615215114

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Carbon-nanotube geometries: analytical and numerical results2017

    • Author(s)
      E. Mainini, H. Murakawa, P. Piovano and U. Stefanelli
    • Journal Title

      Discrete Contin. Dyn. Syst. S

      Volume: 10 Issue: 1 Pages: 141-160

    • DOI

      10.3934/dcdss.2017008

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The Navier-Stokes equations under a unilateral boundary condition of Signorini's type2016

    • Author(s)
      G. Zhou and N. Saito
    • Journal Title

      J. Math. Fluid Mech.

      Volume: 18 Issue: 3 Pages: 481-510

    • DOI

      10.1007/s00021-016-0248-7

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Finite difference approximation for nonlinear Schr\" odinger equations with application to blow-up computation2016

    • Author(s)
      N. Saito and T. Sasaki
    • Journal Title

      Jpn. J. Ind. Appl. Math.

      Volume: 33 Issue: 2 Pages: 427-470

    • DOI

      10.1007/s13160-016-0218-8

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Unilateral problem for the Stokes equations: the well-posedness and finite element approximation2016

    • Author(s)
      N. Saito, Y. Sugitani, and G. Zhou
    • Journal Title

      Appl. Numer. Math.

      Volume: 105 Pages: 124-147

    • DOI

      10.1016/j.apnum.2016.03.002

    • Related Report
      2016 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
  • [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 2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Penalty method with P1/P1 finite element approximation for the Stokes equations under the slip boundary condition2016

    • Author(s)
      Takahito Kashiwabara, Issei Oikawa and Guanyu Zhou
    • Journal Title

      Numerische Mathematik

      Volume: -- Issue: 4 Pages: 705-740

    • DOI

      10.1007/s00211-016-0790-5

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A novel discrete variational derivative method using ``average-difference methods''2016

    • Author(s)
      D. Furihata, S. Sato, T. Matsuo
    • Journal Title

      JSIAM Letters

      Volume: 8 Issue: 0 Pages: 81-84

    • DOI

      10.14495/jsiaml.8.81

    • NAID

      130005434752

    • ISSN
      1883-0609, 1883-0617
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Blow-up of finite-difference solutions to nonlinear wave equations2016

    • Author(s)
      N. Saito, T. Sasaki
    • Journal Title

      J. Math. Sci. Univ. Tokyo

      Volume: 23 Pages: 349-380

    • NAID

      120006906158

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Penalty Method for the Stationary Navier–Stokes Problems Under the Slip Boundary Condition2015

    • Author(s)
      Guanyu Zhou, Takahito Kashiwabara and Issei Oikawa
    • Journal Title

      Journal of Scientific Computing

      Volume: -- Issue: 1 Pages: 339-374

    • DOI

      10.1007/s10915-015-0142-0

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Continuous models for cell-cell adhesion2015

    • Author(s)
      Murakawa, H., and Togashi, H.
    • Journal Title

      Journal of Theoretical Biology

      Volume: 374 Pages: 1-12

    • DOI

      10.1016/j.jtbi.2015.03.002

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Numerical solution of nonlinear cross-diffusion systems by a linear scheme2015

    • Author(s)
      H. Murakawa
    • Journal Title

      Adv. Stud. Pure Math

      Volume: 64 Pages: 243-251

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] A Lyapunov-Type Theorem for Dissipative Numerical Integrators with Adaptive Time-Stepping2015

    • Author(s)
      S. Sato, T. Matsuo, H. Suzuki and D. Furihata
    • Journal Title

      SIAM J. Numer. Anal.

      Volume: 53 Issue: 6 Pages: 2505-2518

    • DOI

      10.1137/140996719

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] 2015An Analysis on The Asymptotic Behavior of Multistep Linearly Implicit Schemes for the Duffing Equation,2015

    • Author(s)
      S. Sato, T. Matsuo, H. Suzuki and D. Furihata
    • Journal Title

      JSIAM Letters

      Volume: 7 Pages: 45-48

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Kato理論の応用としての準線型波動方程式に対する差分法の誤差解析2019

    • Author(s)
      齊藤宣一
    • Organizer
      不連続Galerkin有限要素法の数学理論とその周辺:これからの展開
    • Related Report
      2018 Annual Research Report
  • [Presentation] 急速反応極限,反応拡散系近似,線形近似2019

    • Author(s)
      村川秀樹
    • Organizer
      反応拡散系のパターンダイナミクス2
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 細胞選別現象解明のための個体群動態モデルと表面張力モデル2019

    • Author(s)
      村川秀樹
    • Organizer
      非線形現象の数値シミュレーションと解析2019
    • Related Report
      2018 Annual Research Report
  • [Presentation] 細胞選別を理解するための個体群動態モデルと表面張力モデル2019

    • Author(s)
      村川秀樹
    • Organizer
      反応拡散系と実験の融合
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 反応拡散系の急速反応極限とその応用2019

    • Author(s)
      村川秀樹
    • Organizer
      Nonlinear Evolutionary PDEs and their Equilibrium States II -In honor of the retirement of Professor Yoshio Yamada-
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 散逸型微分方程式の構造保存モデル縮減2019

    • Author(s)
      稲場俊弥・松尾宇泰
    • 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] 高次非線形性を持つ微分方程式に対する安定な陰的線形スキームの構築2019

    • Author(s)
      高橋俊太・松尾宇泰
    • 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] Discontinuous Galerkin method for an N-dimensional spherically symmetric Poisson equation2018

    • Author(s)
      Y. Chiba and N. Saito
    • Organizer
      The 13th SIAM East Asian Section Conference 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Variational analysis of the DG time-stepping method for parabolic equations2018

    • Author(s)
      N. Saito
    • Organizer
      The Seventh China-Japan-Korea Joint Conference on Numerical Mathematics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 滑らかな領域上のRobin境界条件を持つPoisson方程式に対するNitsche法2018

    • Author(s)
      千葉悠喜 齊藤宣一
    • Organizer
      日本応用数理学会 年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 有限要素法による高次元半線形熱方程式の球対称解の数値解析2018

    • Author(s)
      中西徹 齊藤宣一
    • Organizer
      日本応用数理学会 年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 滑らかな領域上のRobin境界条件を持つPoisson方程式に対するNitsche法2018

    • Author(s)
      千葉悠喜 齊藤宣一
    • Organizer
      日本数学会(応用数学分科会)
    • Related Report
      2018 Annual Research Report
  • [Presentation] 有限要素法による高次元半線形熱方程式の球対称解の数値解析2018

    • Author(s)
      中西徹 齊藤宣一
    • Organizer
      日本数学会(応用数学分科会)
    • Related Report
      2018 Annual Research Report
  • [Presentation] Variational analysis of the DG time-stepping method for parabolic equations2018

    • Author(s)
      N. Saito
    • Organizer
      The Japan-Taiwan Joint Workshop on Numerical Analysis and Scientific Computation
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 滑らかな領域上のRobin境界条件に対する有限要素法とDG法2018

    • Author(s)
      千葉悠喜 齊藤宣一
    • Organizer
      応用数学合同研究集会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 有限要素法による高次元半線形熱方程式の球対称解の数値解析2018

    • Author(s)
      中西徹 齊藤宣一
    • Organizer
      応用数学合同研究集会
    • Related Report
      2018 Annual Research Report
  • [Presentation] A population dynamics model of cell-cell adhesion and its applications2018

    • Author(s)
      H. Murakawa
    • Organizer
      Karlstad Applied Analysis Seminar
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Applications of a population dynamics model of cell-cell adhesion2018

    • Author(s)
      H. Murakawa
    • Organizer
      Journee d'Analyse Non Lineaire
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An efficient linear scheme for nonlinear diffusion problems2018

    • Author(s)
      H. Murakawa
    • Organizer
      The Seventh China-Japan-Korea Joint Conference on Numerical Mathematics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A continuous model of cell-cell adhesion and its applications2018

    • Author(s)
      H. Murakawa
    • Organizer
      Czech-Japanese Seminar in Applied Mathematics 2018
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A mathematical model of cell-cell adhesion and its application2018

    • Author(s)
      H. Murakawa
    • Organizer
      The 12th AIMS Conference on Dynamical Systems,Differential Equations and Applications
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Mathematical Modeling of Cell-cell Adhesion and its Applications2018

    • Author(s)
      H. Murakawa
    • Organizer
      Joint Annual Meeting of 70th JSCB and 51st JSDB
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 細胞間接着の数理モデルとその応用2018

    • Author(s)
      村川秀樹
    • Organizer
      第15回 生物数学の理論とその応用 --次世代の数理科学への展開--
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Mathematical modeling of cell-cell adhesion and its applications2018

    • Author(s)
      村川秀樹
    • Organizer
      日本応用数理学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 急速反応極限問題:解析と応用2018

    • Author(s)
      村川秀樹
    • Organizer
      京都大学談話会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Several remarks on $L^\infty$-type error estimates of the finite element method2018

    • Author(s)
      T. Kashiwabara
    • Organizer
      International Workshop on Numerical Methods for Partial Differential Equations
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Semigroup and maximal regularity approach to the primitive equations2018

    • Author(s)
      T. Kashiwabara
    • Organizer
      Conference on Mathematical Fluid Dynamics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The Navier-Stokes equations with slip or leak boundary conditions of friction type2018

    • Author(s)
      Takahito Kashiwabara
    • Organizer
      CoMFoS18
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Penalty method with Crouzeix--Raviart approximation for the Stokes equations under slip boundary condition2018

    • Author(s)
      T Kashiwabara
    • Organizer
      The 7th China-Japan-Korea Joint Conference on Numerical Mathematics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 不連続Galerkin時間離散化法の変分法的な解析2018

    • Author(s)
      齊藤宣一
    • Organizer
      日本数学会(応用数学分科会)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 放物型問題のNitsche’s methodに対するinf-sup条件及び誤差評価について2018

    • Author(s)
      上田祐暉,齊藤宣一
    • Organizer
      日本数学会(応用数学分科会)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Variational analysis of the discontinuous Galerkin time-stepping method for parabolic equations2018

    • Author(s)
      N. Saito
    • Organizer
      International Workshop on Numerical Methods for Partial Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Global strong well-posedness of the primitive equations in $L^\infty_{xy}L^p_z$-type spaces2018

    • Author(s)
      T. Kashiwabara
    • Organizer
      The 15th Japanese-German International Workshop on Mathematical Fluid Dynamics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Finite element analysis for a generalized Robin boundary value problem in a smooth domain2018

    • Author(s)
      T. Kashiwabara
    • Organizer
      Numerical Analysis: Applications to Biomedical Problems and Foundations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 南部括弧に基づく構造保存数値解法に関する一考察2018

    • Author(s)
      杉渕優也 松尾宇泰 佐藤峻
    • Organizer
      日本応用数理学会2018年研究部会連合発表会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 散逸型微分方程式に対する各種モデル縮減手法の検討2018

    • Author(s)
      柳澤広大 松尾宇泰
    • Organizer
      日本応用数理学会2018年研究部会連合発表会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Toward Modern Scientific Computations Based on Structure-Preserving Methods2018

    • Author(s)
      T. Matsuo and Y. Miyatake
    • Organizer
      SIAM PP 2018
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The relation between Crouzeix-Raviart and Raviart-Thomas finite element methods2018

    • Author(s)
      K. Kobayashi
    • Organizer
      International Workshop on Numerical Methods for Partial Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 万能の有限要素はあるか?2018

    • Author(s)
      小林健太
    • Organizer
      北陸応用数理研究会2018
    • Related Report
      2017 Annual Research Report
  • [Presentation] The relation between Crouzeix-Raviart and Raviart-Thomas finite element methods2018

    • Author(s)
      K. Kobayashi
    • Organizer
      Australia New Zealand Industrial and Applied Mathematics 54th Annual Conference
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 細胞間接着の数理モデル2018

    • Author(s)
      村川秀樹
    • Organizer
      自己組織化研究会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 細胞間接着の親和性と細胞パターン形成:数理的アプローチ2018

    • Author(s)
      村川秀樹
    • Organizer
      反応拡散系と実験の融合
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 急速反応極限問題の解析2018

    • Author(s)
      村川秀樹
    • Organizer
      金沢解析セミナー
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 多角形領域上のPoisson方程式に対する不連続Galerkin法の$L^\infty$誤差評価2017

    • Author(s)
      千葉悠喜,齊藤宣一
    • Organizer
      日本数学会
    • Place of Presentation
      首都大学東京(東京都・八王子市)
    • Year and Date
      2017-03-24
    • Related Report
      2016 Annual Research Report
  • [Presentation] 多面体領域上のPoisson方程式に対する不連続Galerkin法の$L^\infty$誤差評価2017

    • Author(s)
      千葉悠喜,齊藤宣一
    • Organizer
      日本応用数理学会2017年研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都・調布市)
    • Year and Date
      2017-03-06
    • 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2017年研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都・調布市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Annual Research Report
  • [Presentation] 後退誤差解析に基づく多段陰的線形スキームの安定化と最適化2017

    • Author(s)
      松尾宇泰, 徐立元
    • Organizer
      日本応用数理学会2017年研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都・調布市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Annual Research Report
  • [Presentation] 偏微分方程式のアジョイント法における離散化2017

    • Author(s)
      田中智規, 松尾宇泰, 伊藤伸一, 長尾大道
    • Organizer
      日本応用数理学会2017年研究部会連合発表会
    • Place of Presentation
      電気通信大学(東京都・調布市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Annual Research Report
  • [Presentation] 界面問題の数値解析手法2017

    • Author(s)
      齊藤宣一
    • Organizer
      研究集会:非線形現象と高精度高品質数値解析
    • Place of Presentation
      富山大学(富山県・富山市)
    • Year and Date
      2017-02-14
    • Related Report
      2016 Annual Research Report
  • [Presentation] Convergence of the immersed-boundary finite-element method for the Stokes problem2017

    • Author(s)
      N. Saito
    • Organizer
      International Conference on Engineering and Computational Mathematics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] L^infty error estimates of discontinuous Galerkin methods for the Poisson equation on a polygonal domain2017

    • Author(s)
      Y. Chiba and N. Saito
    • Organizer
      SIAM East Asian Section Conference 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] N次元球状領域上のPoisson方程式に対する不連続Galerkin法2017

    • Author(s)
      千葉悠喜 齊藤宣一
    • Organizer
      日本応用数理学会 年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] N次元球状領域上のPoisson方程式に対する不連続Galerkin法2017

    • Author(s)
      千葉悠喜 齊藤宣一
    • Organizer
      日本数学会(応用数学分科会)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Banach--Necas--Babuskaの定理とDG time-stepping法2017

    • Author(s)
      齊藤宣一
    • Organizer
      RIMS共同研究(公開型):数値解析学の最前線:理論・方法・応用
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 球対称Poisson方程式に対する不連続Galerkin法の各点評価2017

    • Author(s)
      千葉悠喜 齊藤宣一
    • Organizer
      応用数学合同研究集会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 有限要素法による高次元半線形熱方程式の球対称解の数値計算2017

    • Author(s)
      中西徹,齊藤宣一
    • Organizer
      応用数学合同研究集会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Lax-MilgramからBanach-Necas-Babuskaへ:DG時間離散化法の変分法的な解析2017

    • Author(s)
      齊藤宣一
    • Organizer
      愛媛大学理学部談話会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 数値計算に潜むトラップ2017

    • Author(s)
      齊藤宣一
    • Organizer
      日本応用数理学会・三部会連携「応用数理セミナー」
    • Related Report
      2017 Annual Research Report
  • [Presentation] 不連続ガレルキン時間離散化手法の変分法的な解析2017

    • Author(s)
      齊藤宣一
    • Organizer
      日本応用数理学会・三部会連携「応用数理セミナー」
    • Related Report
      2017 Annual Research Report
  • [Presentation] On the semigroup approach to the primitive equations2017

    • Author(s)
      T. Kashiwabara
    • Organizer
      MFO Workshop, Oberwolfach
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 物理系のシミュレーションにおける構造保存数値解法について2017

    • Author(s)
      松尾宇泰
    • Organizer
      核融合研MHD研究会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On spatial discretization of evolutionary differential equations on the periodic domain with a mixed derivative2017

    • Author(s)
      S. Sato and T. Matsuo
    • Organizer
      SciCADE2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Some structure-preserving discretizations of generalized Ostrovsky equation2017

    • Author(s)
      T. Matsuo
    • Organizer
      SciCADE2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 混合微分を含む発展方程式の空間離散化について2017

    • Author(s)
      佐藤峻 松尾宇泰
    • Organizer
      日本応用数理学会2017年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] ハイブリッド不連続ガレルキン法に基づく構造保存数値解法2017

    • Author(s)
      坪井俊憲 松尾宇泰
    • Organizer
      日本応用数理学会2017年度年会
    • Related Report
      2017 Annual Research Report
  • [Presentation] On some finite-difference based structure-preserving methods for partial differential equations2017

    • Author(s)
      T. Matsuo
    • Organizer
      EASIAM 2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 三角形・四面体上の補間誤差評価とその有限要素法への応用2017

    • Author(s)
      小林健太
    • Organizer
      日本応用数理学会・三部会連携「応用数理セミナー」
    • Related Report
      2017 Annual Research Report
  • [Presentation] Crouzeix-Raviart型有限要素法の誤差解析について2017

    • Author(s)
      小林健太
    • Organizer
      RIMS共同研究(公開型):数値解析学の最前線:理論・方法・応用
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Fast reaction limit : classification and analysis2017

    • Author(s)
      H. Murakawa
    • Organizer
      ReaDiNet 2017: International Conference on Mathematical Biology
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Modeling of cell-cell adhesion and its application2017

    • Author(s)
      H. Murakawa
    • Organizer
      Reaction-Diffusion Systems and Mathematical Modelling in Biology
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification and analysis of fast reaction limit problems2017

    • Author(s)
      H. Murakawa
    • Organizer
      Ito Workshop on Partial Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] An efficient linear scheme for the Stefan problem,the porous medium equation and nonlinear cross-diffusion systems2017

    • Author(s)
      H. Murakawa
    • Organizer
      Equadiff2017
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Numerical analysis for nonlinear diffusion problems2017

    • Author(s)
      村川秀樹
    • Organizer
      RIMS共同研究 数値解析学の最前線 :理論・方法・応用
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 急速反応極限問題の分類と解析2017

    • Author(s)
      村川秀樹
    • Organizer
      RIMS共同研究 非線形現象と反応拡散方程式
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Error analysis of Lagrange interpolation on tetrahedrons2017

    • Author(s)
      Kenta Kobayashi
    • Organizer
      Australia New Zealand Industrial and Applied Mathematics 53th Annual Conference
    • Place of Presentation
      ハーンドルフ(オーストラリア)
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 有限要素法における$L^\infty$型誤差評価と離散グリーン関数について2016

    • Author(s)
      柏原崇人
    • Organizer
      日本数学会
    • Place of Presentation
      関西大学(大阪府・吹田市)
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Error analysis of Lagrange interpolation on tetrahedrons2016

    • Author(s)
      小林健太, 土屋卓也
    • Organizer
      日本数学会
    • Place of Presentation
      関西大学(大阪府・吹田市)
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] 非凸多面体領域におけるPoisson方程式の有限要素法の$L^\infty$評価2016

    • Author(s)
      千葉悠喜,齊藤宣一
    • Organizer
      日本応用数理学会
    • Place of Presentation
      北九州国際会議場(福岡県・北九州市)
    • Year and Date
      2016-09-12
    • 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
    • Place of Presentation
      北九州国際会議場(福岡県・北九州市)
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
  • [Presentation] $W^{1,\infty}$-error Analysis of the Finite Element Method in a Smooth Domain2016

    • Author(s)
      T. Kashiwabara
    • Organizer
      EASIAM 2016
    • Place of Presentation
      マカオ(中国)
    • Year and Date
      2016-06-20
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A modified model of cell-cell adhesion2016

    • Author(s)
      H. Murakawa
    • Organizer
      ALGORITMY 2016 Conference on Scientific Computing
    • Place of Presentation
      Podbanske(スロバキア)
    • Year and Date
      2016-03-17
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 楕円型界面問題に対するハイブリッド型不連続Galerkin法2016

    • Author(s)
      宮下大,齊藤宣一
    • Organizer
      日本応用数理学会
    • Place of Presentation
      神戸学院大学
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] 移流拡散方程式に対する不連続Galerkin法の理論解析における注意2016

    • Author(s)
      千葉悠喜,齊藤宣一
    • Organizer
      日本応用数理学会
    • Place of Presentation
      神戸学院大学
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] 埋め込み境界法の数学的定式化に対する諸注意2016

    • Author(s)
      杉谷宜紀,齊藤宣一
    • Organizer
      日本応用数理学会
    • Place of Presentation
      神戸学院大学
    • Year and Date
      2016-03-04
    • Related Report
      2015 Annual Research Report
  • [Presentation] A norm-preserving self-adaptive moving mesh integrator for the short-pulse equation2015

    • Author(s)
      S. Sato, T. Matsuo, and B.-F. Feng
    • Organizer
      数理解析研究所研究集会「現象解明に向けた数値解析学の新展開
    • Place of Presentation
      京大RIMS
    • Year and Date
      2015-11-18
    • Related Report
      2015 Annual Research Report
  • [Presentation] 数値計算における「構造保存」の考え方について2015

    • Author(s)
      松尾宇泰
    • Organizer
      数理解析研究所研究集会「現象解明に向けた数値解析学の新展開
    • Place of Presentation
      京大RIMS
    • Year and Date
      2015-11-18
    • Related Report
      2015 Annual Research Report
  • [Presentation] Modeling and analysis of cell-cell adhesion2015

    • Author(s)
      H. Murakawa
    • Organizer
      International conference on mathematical modeling and applications 2015 Self-Organization Modeling and Analysis
    • Place of Presentation
      明治大学
    • Year and Date
      2015-10-26
    • Related Report
      2015 Annual Research Report
  • [Presentation] 有限要素法の誤差解析と精度保証付き数値計算2015

    • Author(s)
      小林健太
    • Organizer
      東京理科大学理工学部数学科談話会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2015-10-13
    • Related Report
      2015 Annual Research Report
  • [Presentation] Discrete maximal regularity for abstract Cauchy problems and its application to the finite element method,2015

    • Author(s)
      T. Kemmochi and N. Saito
    • Organizer
      The 8th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      Beijing(中国)
    • Year and Date
      2015-08-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Analysis of space-time computation technique with continuous representation in time (ST-C),2015

    • Author(s)
      Y. Ueda and N. Saito
    • Organizer
      The 8th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      Beijing(中国)
    • Year and Date
      2015-08-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Finite element approximation for the Stokes equations under a unilateral boundary condition2015

    • Author(s)
      Y. Sugitani, G. Zhou and N. Saito
    • Organizer
      The 8th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      Beijing(中国)
    • Year and Date
      2015-08-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Blow-up of finite difference solutions to nonlinear Schrodinger equations2015

    • Author(s)
      T. Sasaki and N. Saito
    • Organizer
      The 8th International Congress on Industrial and Applied Mathematics
    • Place of Presentation
      Beijing(中国)
    • Year and Date
      2015-08-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Funded Workshop] The Seventh China-Japan-Korea Joint Conference on Numerical Mathematics2018

    • Related Report
      2018 Annual Research Report

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Published: 2015-04-16   Modified: 2020-03-30  

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