Publications/Talks

Publications

* Corresponding author

Submitted preprints

[S2] H. Ishizaka: Coming soon. [Arxiv] [DOI]

[S1] H. Ishizaka*: On discrete Sobolev inequalities for nonconforming finite elements under a semi-regular mesh condition. (2025) [Arxiv] [DOI]

Publications in peer-reviewed journals

[10] H. Ishizaka*: Nitsche's method under a semi-regular mesh condition. Numerical Algorithms, (2025) [Arxiv] [DOI]

[9] H. Ishizaka*: Anisotropic modified Crouzeix-Raviart finite element method for the stationary Navier-Stokes equation. Numerische Mathematik 157, 855-895 (2025) [Arxiv] [DOI]

[8] H. Ishizaka*: Morley finite element analysis for fourth-order elliptic equations under a semi-regular mesh condition. Applications of Mathematics 69 (6), 769-805 (2024) [Arxiv] [DOI]

[7] H. Ishizaka*: Hybrid weakly over-penalised symmetric interior penalty method on anisotropic meshes. Calcolo 61, 45 (2024) [Arxiv] [DOI]

[6] H. Ishizaka*: Anisotropic weakly over-penalised symmetric interior penalty method for the Stokes equation. Journal of Scientific Computing 100, 53 (2024) [Arxiv] [DOI]

[5] H. Ishizaka*, K. Kobayashi, T. Tsuchiya: Anisotropic interpolation error estimates using a new geometric parameter. Jpn. J. Ind. Appl. Math. 40 (1), 475-512 (2023) [Japan Journal of Industrial and Applied Mathematics] [DOI]

[4] H. Ishizaka*: Anisotropic Raviart-Thomas interpolation error estimates using a new geometric parameter. Calcolo, 59 (4), (2022) [Arxiv] [Calcolo] [DOI]

[3] H. Ishizaka, K. Kobayashi, R. Suzuki, T. Tsuchiya: A new geometric condition equivalent to the maximum angle condition for tetrahedrons. Computers & Mathematics with Applications 99, 323-328 (2021) [Computers & Mathematics with Applications] [DOI]

[2] H. Ishizaka*, K. Kobayashi, T. Tsuchiya: Crouzeix-Raviart and Raviart-Thomas finite-element error analysis on anisotropic meshes violating the maximum-angle condition. Jpn. J. Ind. Appl. Math. 38 (2), 645-675 (2021) [ResearchGate] [DOI]

[1] H. Ishizaka*, K. Kobayashi, T. Tsuchiya: General theory of interpolation error estimates on anisotropic meshes. Jpn. J. Ind. Appl. Math. 38 (1), 163-191 (2021) [ResearchGate] [DOI]
Correction to: General theory of interpolation error estimates on anisotropic meshes. [Link]

Notes

[N2] H. Ishizaka: Interpolation error analysis using a new geometric parameter. [Arxiv]

[N1] H. Ishizaka: Note on a weakly over-penalised symmetric interior penalty method on anisotropic meshes for the Poisson equation, Ver. 1. [Arxiv]

Ongoing Papers, Next Topics

[O6] H. Ishizaka: (temporary title)

[O5] H. Ishizaka: (temporary title)

[O4] H. Ishizaka: (temporary title)

[O3] H. Ishizaka: (temporary title)

[O2] H. Ishizaka: (temporary title)

[O1] H. Ishizaka: (temporary title)

Presentations

[P4] H. Ishizaka and T. Tsuchiya, Error analysis of Crouzeix–Raviart finite element methods on anisotropic meshes, Joint Conference on Applied Mathematics, The Mathematical Society of Japan, 12 December 2019, Ryukoku University, Shiga

[P3] H. Ishizaka and T. Tsuchiya, Error analysis of Crouzeix-Raviart finite element method without the shape regularity condition, The Mathematical Society of Japan, 17 September 2019, Kanazawa University, Ishikawa

[P2] H. Ishizaka and T. Tsuchiya, Error analysis of Crouzeix-Raviart finite element method without the shape regularity condition, The Japan Society for Industrial and Applied Mathematics, 03 September 2019, Tokyo University, Tokyo

[P1] H. Ishizaka and M. Tabata, An finite element analysis of the two-dimensional micro scale heat transport equations, The Japan Society for Industrial and Applied Mathematics, March 2007, Nagoya University, Aichi

Theses

[PhD Thesis] Anisotropic interpolation error analysis using a new geometric parameter and its applications

[Master Thesis] Mathematical analysis of a linearised equation accompanied with a two-phase flow problem

Classification

Crouzeix-Raviart FEMs

Papers: [2][9][10][PhD Thesis]

Presentations: [P2][P3][P4]

Notes: [N2]

Discontinuous Galerkin FEMs, WOPSIP type, Hybrid type

Papers: [6][7]

Presentations:

Notes: [N1]

Morley FEMs

Papers: [8]

Presentations:

Notes: [N2]

Anisotropic Interpolation Error Estimates

Papers: [1][3][4][5][8][9][PhD Thesis]

Presentations: [P2][P3][P4]

Notes: [N2]

Anisotropic FEMs

Papers: [2][6][7][8][9][10][PhD Thesis]

Presentations: [P2][P3][P4]

Notes: [N1]

Pressure robust (well-balanced) schemes

Papers: [8][9][10]

Presentations:

FEMs for the non-Fourier heat transfer equation

Papers:

Presentation: [P1]

Mathematical analysis of two-phase flow problems

Paper: [Master Thesis]

Presentation:

Mathematical analysis of Moving boundary problems

Paper:

Presentation: