Numerical Analysis of an Optimal Control Problem Governed by the Stationary Navier-Stokes Equations with Global Velocity-Constrained
Year: 2018
Author: Haifeng Niu, Danping Yang, Jianwei Zhou
Communications in Computational Physics, Vol. 24 (2018), Iss. 5 : pp. 1477–1502
Abstract
A state-constrained optimal control problem governed by the stationary Navier-Stokes equations is studied. Finite element approximation is constructed, the optimal-order a priori H1-norm and L2-norm error estimates are given, for which the optimal state is a nonsingular solution of the Navier-Stokes equations to the optimal control.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0045
Communications in Computational Physics, Vol. 24 (2018), Iss. 5 : pp. 1477–1502
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Optimal control state-constrained Navier-Stokes finite element error estimates.
Author Details
-
Primary Hyperparathyroidism Across the Age Spectrum: A Comparative Study of Clinical and Biochemical Profiles in Older and Younger Patients
Evranos Öğmen, Berna | İnce, Nurcan | Topaloğlu, Oya | Ersoy, Reyhan | Çakır, BekirEuropean Journal of Geriatrics and Gerontology, Vol. (2025), Iss.
https://doi.org/10.4274/ejgg.galenos.2025.2024-11-8 [Citations: 0] -
Two‐level multiscale enrichment finite volume method based on the Newton iteration for the stationary incompressible magnetohydrodynamics flow
Shen, Xiaorong | Chen, Chuanjun | Bian, Huanying | Zhang, TongMathematical Methods in the Applied Sciences, Vol. (2023), Iss.
https://doi.org/10.1002/mma.9630 [Citations: 0] -
Two‐grid mixed finite element method for two‐dimensional time‐dependent Schrödinger equation
Tian, Zhikun | Chen, Yanping | Huang, Yunqing | Wang, JianyunMathematical Methods in the Applied Sciences, Vol. 46 (2023), Iss. 12 P.12759
https://doi.org/10.1002/mma.9210 [Citations: 2] -
Approximate controllability of linear parabolic equation with memory
Kumar, Anil | Pani, Amiya K. | Joshi, Mohan C.Computers & Mathematics with Applications, Vol. 128 (2022), Iss. P.320
https://doi.org/10.1016/j.camwa.2022.11.003 [Citations: 1] -
$$\beta $$-robust virtual element method for distributed order time-fractional reaction-diffusion equation with variable coefficients
Chen, Yanping | Lei, Jian | Gu, Qiling | Zhou, Jianwei | Qin, FangfangNumerical Algorithms, Vol. (2025), Iss.
https://doi.org/10.1007/s11075-025-02052-6 [Citations: 0] -
An efficient Legendre-Galerkin approximation for the fourth-order equation with singular potential and SSP boundary condition
Zou, Shuimu | Zhang, JunOpen Mathematics, Vol. 21 (2023), Iss. 1
https://doi.org/10.1515/math-2023-0128 [Citations: 0] -
A novel Chebyshev-collocation spectral method for solving the transport equation
Li, Zhonghui | Chen, Xiangyong | Qiu, Jianlong | Xia, TongshuiJournal of Industrial & Management Optimization, Vol. 17 (2021), Iss. 5 P.2519
https://doi.org/10.3934/jimo.2020080 [Citations: 1] -
A Legendre spectral method based on a hybrid format and its error estimation for fourth-order eigenvalue problems
Chen, Yuanqiang | Zheng, Jihui | An, JingAIMS Mathematics, Vol. 9 (2024), Iss. 3 P.7570
https://doi.org/10.3934/math.2024367 [Citations: 0] -
Spectral approximation for optimal control problems governed by first bi‐harmonic equation
Lin, Xiuxiu | Chen, Yanping | Huang, YunqingNumerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 4 P.2808
https://doi.org/10.1002/num.22988 [Citations: 1] -
Optimal error estimates of two‐level iterative finite element methods for the thermally coupled incompressible MHD with different viscosities
Zhang, Huifang | Zhang, TongMathematical Methods in the Applied Sciences, Vol. 48 (2025), Iss. 7 P.7109
https://doi.org/10.1002/mma.8800 [Citations: 0] -
A Difference Scheme and Its Error Analysis for a Poisson Equation with Nonlocal Boundary Conditions
Feng, Chunsheng | Nie, Cunyun | Yu, Haiyuan | Zhou, Liping | Rajagopal, KarthikeyanComplexity, Vol. 2020 (2020), Iss. P.1
https://doi.org/10.1155/2020/6329404 [Citations: 1] -
An efficient Fourier spectral method and error analysis for the fourth order problem with periodic boundary conditions and variable coefficients
Jiang, Tingting | Jiang, Jiantao | An, JingAIMS Mathematics, Vol. 8 (2023), Iss. 4 P.9585
https://doi.org/10.3934/math.2023484 [Citations: 0] -
Novel efficient iterative schemes for linear finite element approximations of elliptic optimal control problems with integral constraint on the state
Ge, Liang | Huang, Jian | Zhou, JianweiJournal of Computational and Applied Mathematics, Vol. 456 (2025), Iss. P.116225
https://doi.org/10.1016/j.cam.2024.116225 [Citations: 0] -
Two‐grid finite element method on grade meshes for time‐fractional nonlinear Schrödinger equation
Hu, Hanzhang | Chen, Yanping | Zhou, JianweiNumerical Methods for Partial Differential Equations, Vol. 40 (2024), Iss. 2
https://doi.org/10.1002/num.23073 [Citations: 7] -
Method of Particular Solutions for Second-Order Differential Equation with Variable Coefficients via Orthogonal Polynomials
Xie, Huantian | Zhang, Zhaozhong | Jiang, Ziwu | Zhou, Jianwei | Gurefe, YusufJournal of Function Spaces, Vol. 2023 (2023), Iss. P.1
https://doi.org/10.1155/2023/9748605 [Citations: 1] -
A novel mixed spectral approximation for fourth-order problems with Neumann boundary conditions
Wang, Qingzhu | Zheng, Jihui | An, JingInternational Journal of Computer Mathematics, Vol. (2025), Iss. P.1
https://doi.org/10.1080/00207160.2025.2469246 [Citations: 0]