Mitsuhiro T. Nakao

Publication Activity (10 Years)

Years Active: 1997-2023
Publications (10 Years): 16

Top Topics

Boundary Value Problem

Error Estimates

Top Venues

J. Comput. Appl. Math.

SIAM J. Numer. Anal.

Numerische Mathematik

Publications

Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao
Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces. J. Sci. Comput. 94 (2) (2023)
Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao
Inclusion method of optimal constant with quadratic convergence for H01-projection error estimates and its applications. J. Comput. Appl. Math. 417 (2023)
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
Improvement of the Constructive A Priori Error Estimates for a Fully Discretized Periodic Solution of Heat Equation. Comput. Methods Appl. Math. 22 (3) (2022)
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators. Acta Cybern. 26 (1) (2022)
Xuefeng Liu, Mitsuhiro T. Nakao, Shin'ichi Oishi
Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains. Commun. Nonlinear Sci. Numer. Simul. 108 (2022)
Xuefeng Liu, Mitsuhiro T. Nakao, Shin'ichi Oishi
Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains. CoRR (2021)
Makoto Mizuguchi, Mitsuhiro T. Nakao, Kouta Sekine, Shin'ichi Oishi
Error Constants for the Semi-Discrete Galerkin Approximation of the Linear Heat Equation. J. Sci. Comput. 89 (2) (2021)
Mitsuhiro T. Nakao, Takeshi Ogita, Siegfried M. Rump
Foreword. J. Comput. Appl. Math. 382 (2021)
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
Constructive error estimates for full discrete approximation of periodic solution for heat equation. J. Comput. Appl. Math. 368 (2020)
Xuefeng Liu, Mitsuhiro T. Nakao, Chun'guang You, Shin'ichi Oishi
Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations. CoRR (2020)
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space. J. Comput. Appl. Math. 369 (2020)
Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi
A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator. Numerische Mathematik 146 (4) (2020)
Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi
A new formulation for the numerical proof of the existence of solutions to elliptic problems. CoRR (2019)
Yoshitaka Watanabe, Mitsuhiro T. Nakao, Kaori Nagatou
On the compactness of a nonlinear operator related to stream function-vorticity formulation for the Navier-Stokes equations. JSIAM Lett. 9 (2017)
Yoshitaka Watanabe, Mitsuhiro T. Nakao
A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration. Appl. Math. Comput. 276 (2016)
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
Regularities of the Poisson Equation on Polygonal Domains. MACIS (2015)
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao
Some Remarks on the Rigorous Estimation of Inverse Linear Elliptic Operators. SCAN (2014)
Yoshitaka Watanabe, Kaori Nagatou, Michael Plum, Mitsuhiro T. Nakao
Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces. SIAM J. Numer. Anal. 52 (2) (2014)
Takehiko Kinoshita, Takuma Kimura, Mitsuhiro T. Nakao
On the a posteriori estimates for inverse operators of linear parabolic equations with applications to the numerical enclosure of solutions for nonlinear problems. Numerische Mathematik 126 (4) (2014)
Mitsuhiro T. Nakao, Takuma Kimura, Takehiko Kinoshita
Constructive A Priori Error Estimates for a Full Discrete Approximation of the Heat Equation. SIAM J. Numer. Anal. 51 (3) (2013)
Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao
A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations. Math. Comput. 82 (283) (2013)
Takehiko Kinoshita, Mitsuhiro T. Nakao
Some Remarks on the Optimal Error Estimates for the Finite Element Method on the L-Shaped Domain. ITNG (2013)
Mitsuhiro T. Nakao, Takehiko Kinoshita, Takuma Kimura
On a posteriori estimates of inverse operators for linear parabolic initial-boundary value problems. Computing 94 (2-4) (2012)
Takehiko Kinoshita, Takuma Kimura, Mitsuhiro T. Nakao
A posteriori estimates of inverse operators for initial value problems in linear ordinary differential equations. J. Comput. Appl. Math. 236 (6) (2011)
Takehiko Kinoshita, Mitsuhiro T. Nakao
-projection. J. Comput. Appl. Math. 234 (2) (2010)
Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida, Myoung-Nyoung Kim
Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems. J. Sci. Comput. 43 (3) (2010)
Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida, Myoungnyoun Kim
Erratum to: Computer Assisted Proofs of Bifurcating Solutions for Nonlinear Heat Convection Problems. J. Sci. Comput. 44 (1) (2010)
Teruya Minamoto, Mitsuhiro T. Nakao
A numerical verification method for a periodic solution of a delay differential equation. J. Comput. Appl. Math. 235 (3) (2010)
Myoungnyoun Kim, Mitsuhiro T. Nakao, Yoshitaka Watanabe, Takaaki Nishida
A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems. Numerische Mathematik 111 (3) (2009)
Mitsuhiro T. Nakao, Takehiko Kinoshita
On very accurate verification of solutions for boundary value problems by using spectral methods. JSIAM Lett. 1 (2009)
Mitsuhiro T. Nakao, Takehiko Kinoshita
Some remarks on the behaviour of the finite element solution in nonsmooth domains. Appl. Math. Lett. 21 (12) (2008)
Mitsuhiro T. Nakao, Kaori Nagatou
. Reliab. Comput. 11 (2) (2005)
Mitsuhiro T. Nakao, Kouji Hashimoto, Yoshitaka Watanabe
A Numerical Method to Verify the Invertibility of Linear Elliptic Operators with Applications to Nonlinear Problems. Computing 75 (1) (2005)
Mitsuhiro T. Nakao, Yoshitaka Watanabe
An Efficient Approach to the Numerical Verification for Solutions of Elliptic Differential Equations. Numer. Algorithms 37 (1-4) (2004)
Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida
Some Computer Assisted Proofs for Solutions of the Heat Convection Problems. Reliab. Comput. 9 (5) (2003)
Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao
A Numerical Verification Method of Solutions for the Navier-Stokes Equations. Reliab. Comput. 5 (3) (1999)
Mitsuhiro T. Nakao, Nobito Yamamoto, Yoshitaka Watanabe
Constructive L2 Error Estimates for Finite Element Solutions of the Stokes Equations. Reliab. Comput. 4 (2) (1998)
Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao
A Numerical Verification Method of Solutions for the Navier-Stokes Equations. SCAN (1998)
Cheon Seoung Ryoo, Mitsuhiro T. Nakao
Numerical verification of solutions for variational inequalities. Numerische Mathematik 81 (2) (1998)
Teruya Minamoto, Mitsuhiro T. Nakao
Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case. Reliab. Comput. 3 (2) (1997)