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Improved parallel finite element methods for the stationary Navier–Stokes problem

Numerical Algorithms
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Guangzhi Du, Liyun Zuo
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The linearized non-stationary problem for the permeable boundary Navier–Stokes flows

Applied Mathematics and Computation, 2004
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An analysis of a weak Galerkin finite element method for stationary Navier–Stokes problems

Journal of Computational and Applied Mathematics, 2019
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Tie Zhang, Tao Lin 0003
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On a posteriori error estimates for the stationary Navier-Stokes problem

Journal of Mathematical Sciences, 2008
We obtain a computable upper bound for the difference between a solution to the stationary Navier-Stokes problem and any solenoidal vector-valued function satisfying the boundary condition and possessing necessary differentiability properties. For sufficiently small velocities this estimate implies an estimate of the deviation from exact solution in ...
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Penalty Method for the Stationary Navier–Stokes Problems Under the Slip Boundary Condition

Journal of Scientific Computing, 2015
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Guanyu Zhou   +2 more
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An estimate of the solutions of a stationary problem for the Navier-Stokes equations

Journal of Mathematical Sciences, 2000
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Existence of an Optimal Solution of a Shape Control Problem for the Stationary Navier--Stokes Equations

SIAM Journal on Control and Optimization, 1998
This paper is concerned with an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag.
Max Gunzburger
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Exterior problem for the stationary Navier-Stokes equations in the Lorentz space

Mathematische Annalen, 1998
Let \(\Omega\) be an exterior domain in \(\mathbb{R}^n, n\geqslant 3\), with a smooth boundary. The stationary Navier-Stokes system is considered \[ \begin{aligned} -&\Delta v+v\cdot\nabla v+\nabla p=\text{div} F,\quad \nabla\cdot v=0 \quad \text{in \;} \Omega,\\&v=0 \quad \text{on }\partial \Omega,\quad \lim_{|x|\to\infty}v(x)=0.\end{aligned} \] Here \
Kozono, Hideo, Yamazaki, Masao
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Numerical resolution of optimal control problem for the in-stationary Navier–Stokes equations

Journal of Inverse and Ill-posed Problems, 2018
Abstract In this paper we present a study of optimal control problem for the unsteady Navier–Stokes equations. We discuss the existence of the solution, adopt a new numerical resolution for this problem and combine Euler explicit scheme in time and both of methods spectral and finite elements in space.
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Multiscale enrichment of a finite volume element method for the stationary Navier–Stokes problem

International Journal of Computer Mathematics, 2013
In this paper, we introduce a finite volume element method for the Navier–Stokes problem. This method is based on the multiscale enrichment and uses the lowest finite element pair P1/P0. The stability and convergence of the optimal order in H1-norm for velocity and L2-norm for pressure are obtained.
Juan Wen, Yinnian He, Jianhong Yang
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