The verified computing with assistance of computers has proved to be a promising approach to investigate the solution existence to nonlinear equation systems. In this paper, the latest progress about the solution verification for the stationary Navier--Stokes equationover a non-convex 3D domain is reported .
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 the exact solution as the fixed point of the Newton iteration exists around the approximate solution through rigorous computation and error estimation. The explicit values of quantities required by applying the fixed point theorem are obtained by utilizing newly developed quantitative error estimation for finite element solutions to boundary value problems and eigenvalue problems of the Stokes equation .
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The verified computing with assistance of computers has proved to be a promising approach to investigate the solution existence to nonlinear equation systems. In this paper, the latest progress about the solution verification for the stationary Navier--Stokes equationover a non-convex
This paper proposes a computer-assisted solution existence verification method for the stationary Navier-Stokes equation over general
R
domain is reported
domains. The proposed method verifies that the exact solution as the fixed point of the Newton iteration exists around the approximate solution through rigorous computation and error estimation. The explicit values of quantities required by applying the fixed point theorem are obtained by utilizing newly developed quantitative error estimation for finite element solutions to boundary value problems and eigenvalue problems of the Stokes equation