3 papers
math.NA2020
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…
math.NA2019
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…
math.NA2018
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…