9 citations · 28 across the 6 of their papers we have counts for
6 papers
Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains
Xuefeng Liu, Mitsuhiro T. Nakao, Shin'ichi Oishi
This paper proposes a computer-assisted solution existence verification method for the stationary Navier-Stokes equation over general 3D domains. The proposed method verifies that…
Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations
Xuefeng Liu, Mitsuhiro Nakao, Chun'guang You +1
For the Stokes equation over 2D and 3D domains, explicit a posteriori and a priori error estimation are novelly developed for the finite element solution. The difficulty in handlin…
A new formulation for the numerical proof of the existence of solutions to elliptic problems
Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi
Infinite-dimensional Newton methods can be effectively used to derive numerical proofs of the existence of solutions to partial differential equations (PDEs). In computer-assisted…
Constructive a priori error estimates for a full discrete approximation of periodic solutions for the heat equation
Takuma Kimura, Teruya Minamoto, Mitsuhiro T. Nakao
We consider the constructive a priori error estimates for a full discrete numerical solution of the heat equation with time-periodic condition.
Numerical verification of solutions for nonlinear parabolic problems
Kouji Hashimoto, Takehiko Kinoshita, Mitsuhiro T. Nakao
In this paper, we present a numerical verification method of solutions for nonlinear parabolic initial boundary value problems. Decomposing the problem into a nonlinear part and an…
Constructive error analysis of a full-discrete finite element method for the heat equation
Kouji Hashimoto, Mitsuhiro T. Nakao, Takuma Kimura +1
In this paper, we present a new full-discrete finite element method for the heat equation, and show the numerical stability of the method by verified computations. Since, in the er…