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ORCIDMitsuhiro T. Nakao
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2020 – today
- 2023
[j33]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: 114521 (2023)- [j32]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): 43 (2023) - 2022
- [j31]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): 71-82 (2022) - [j30]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): 631-647 (2022) - [j29]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: 106223 (2022) - 2021
- [j28]Mitsuhiro T. Nakao, Takeshi Ogita, Siegfried M. Rump:
Foreword. J. Comput. Appl. Math. 382: 113078 (2021) - [j27]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): 34 (2021) - [i3]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 abs/2101.03727 (2021) - 2020
- [j26]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) - [j25]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) - [j24]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): 907-926 (2020) - [i2]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 abs/2006.02952 (2020)
2010 – 2019
- 2019
- [i1]Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi:
A new formulation for the numerical proof of the existence of solutions to elliptic problems. CoRR abs/1910.00759 (2019) - 2017
- [j23]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: 77-80 (2017) - 2016
- [j22]Yoshitaka Watanabe, Mitsuhiro T. Nakao:
A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration. Appl. Math. Comput. 276: 239-251 (2016) - 2015
- [c4]Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao:
H3 and H4 Regularities of the Poisson Equation on Polygonal Domains. MACIS 2015: 199-201 - 2014
- [j21]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): 679-701 (2014) - [j20]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): 975-992 (2014) - [c3]Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao:
Some Remarks on the Rigorous Estimation of Inverse Linear Elliptic Operators. SCAN 2014: 225-235 - 2013
- [j19]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): 1543-1557 (2013) - [j18]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): 1525-1541 (2013) - [c2]Takehiko Kinoshita, Mitsuhiro T. Nakao:
Some Remarks on the Optimal Error Estimates for the Finite Element Method on the L-Shaped Domain. ITNG 2013: 173-178 - 2012
- [j17]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): 151-162 (2012) - 2011
- [j16]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): 1622-1636 (2011) - 2010
- [j15]Takehiko Kinoshita, Mitsuhiro T. Nakao:
On very accurate enclosure of the optimal constant in the a priori error estimates for H20-projection. J. Comput. Appl. Math. 234(2): 526-537 (2010) - [j14]Teruya Minamoto, Mitsuhiro T. Nakao:
A numerical verification method for a periodic solution of a delay differential equation. J. Comput. Appl. Math. 235(3): 870-878 (2010) - [j13]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): 388-401 (2010) - [j12]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): 107 (2010)
2000 – 2009
- 2009
- [j11]Mitsuhiro T. Nakao, Takehiko Kinoshita:
On very accurate verification of solutions for boundary value problems by using spectral methods. JSIAM Lett. 1: 21-24 (2009) - [j10]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): 389-406 (2009) - 2008
- [j9]Mitsuhiro T. Nakao, Takehiko Kinoshita:
Some remarks on the behaviour of the finite element solution in nonsmooth domains. Appl. Math. Lett. 21(12): 1310-1314 (2008) - 2005
- [j8]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): 1-14 (2005) - [j7]Mitsuhiro T. Nakao, Kaori Nagatou:
SCAN'2004 11th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic, and Validated NumericsFukuoka, Japan, October 4-8, 2004. Reliab. Comput. 11(2): 157-159 (2005) - 2004
- [j6]Mitsuhiro T. Nakao, Yoshitaka Watanabe:
An Efficient Approach to the Numerical Verification for Solutions of Elliptic Differential Equations. Numer. Algorithms 37(1-4): 311-323 (2004) - 2003
- [j5]Mitsuhiro T. Nakao, Yoshitaka Watanabe, Nobito Yamamoto, Takaaki Nishida:
Some Computer Assisted Proofs for Solutions of the Heat Convection Problems. Reliab. Comput. 9(5): 359-372 (2003) - 2001
- [p1]Mitsuhiro T. Nakao, Nobito Yamamoto:
A Guaranteed Bound of the Optimal Constant in the Error Estimates for Linear Triangular Elements. Perspectives on Enclosure Methods 2001: 265-275
1990 – 1999
- 1999
- [j4]Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao:
A Numerical Verification Method of Solutions for the Navier-Stokes Equations. Reliab. Comput. 5(3): 347-357 (1999) - 1998
- [j3]Cheon Seoung Ryoo, Mitsuhiro T. Nakao:
Numerical verification of solutions for variational inequalities. Numerische Mathematik 81(2): 305-320 (1998) - [j2]Mitsuhiro T. Nakao, Nobito Yamamoto, Yoshitaka Watanabe:
Constructive L2 Error Estimates for Finite Element Solutions of the Stokes Equations. Reliab. Comput. 4(2): 115-124 (1998) - [c1]Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao:
A Numerical Verification Method of Solutions for the Navier-Stokes Equations. SCAN 1998: 347-357 - 1997
- [j1]Teruya Minamoto, Mitsuhiro T. Nakao:
Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case. Reliab. Comput. 3(2): 137-147 (1997)
Coauthor Index
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