A projection-based variational multiscale method for the optimal control problems governed by the stationary Navier–Stokes equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2016.03.005 ◽

2016 ◽

Vol 106 ◽

pp. 116-128

Author(s):

Fikriye Yılmaz ◽

Aytekin Çıbık

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Stokes Equations ◽

Multiscale Method ◽

Navier Stokes ◽

Control Problems ◽

Variational Multiscale Method ◽

Navier Stokes Equations ◽

Variational Multiscale ◽

Stationary Navier Stokes Equations

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Second-Order Optimality Conditions and Solution Stability to Optimal Control Problems Governed by Stationary Navier-Stokes Equations

Acta Mathematica Vietnamica ◽

10.1007/s40306-018-00304-3 ◽

2018 ◽

Vol 44 (2) ◽

pp. 431-448 ◽

Author(s):

Bui Trong Kien

Keyword(s):

Optimal Control ◽

Optimality Conditions ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Control Problems ◽

Solution Stability ◽

Navier Stokes Equations ◽

Second Order Optimality Conditions ◽

Stationary Navier Stokes Equations

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Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls

Mathematics of Computation ◽

10.1090/s0025-5718-1991-1079020-5 ◽

1991 ◽

Vol 57 (195) ◽

pp. 123-123 ◽

Author(s):

M. D. Gunzburger ◽

L. Hou ◽

T. P. Svobodny

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

Stokes Equations ◽

Finite Element Approximation ◽

Navier Stokes ◽

Control Problems ◽

Element Approximation ◽

Navier Stokes Equations ◽

Stationary Navier Stokes Equations

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Variational multiscale method based on the Crank–Nicolson extrapolation scheme for the non-stationary Navier–Stokes equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2012.704023 ◽

2012 ◽

Vol 89 (16) ◽

pp. 2198-2223 ◽

Author(s):

Li Shan ◽

Yanren Hou ◽

Haibiao Zheng

Keyword(s):

Stokes Equations ◽

Multiscale Method ◽

Navier Stokes ◽

Variational Multiscale Method ◽

Navier Stokes Equations ◽

Variational Multiscale ◽

Extrapolation Scheme ◽

Stationary Navier Stokes Equations ◽

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First- and Second-Order Necessary Optimality Conditions for Optimal Control Problems Governed by Stationary Navier–Stokes Equations with Pure State Constraints

Vietnam Journal of Mathematics ◽

10.1007/s10013-015-0173-8 ◽

2015 ◽

Vol 44 (1) ◽

pp. 103-131 ◽

Author(s):

Bui Trong Kien ◽

Gue Myung Lee ◽

Nguyen Hai Son

Keyword(s):

Optimal Control ◽

State Constraints ◽

Optimal Control Problems ◽

Stokes Equations ◽

Necessary Optimality Conditions ◽

Navier Stokes ◽

Control Problems ◽

Navier Stokes Equations ◽

Pure State Constraints ◽

Stationary Navier Stokes Equations

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Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls

ESAIM Mathematical Modelling and Numerical Analysis ◽

10.1051/m2an/1991250607111 ◽

1991 ◽

Vol 25 (6) ◽

pp. 711-748 ◽

Author(s):

M. D. Gunzburger ◽

L. S. Hou ◽

Th. P. Svobodny

Keyword(s):

Optimal Control ◽

Finite Element ◽

Optimal Control Problems ◽

Stokes Equations ◽

Finite Element Approximation ◽

Navier Stokes ◽

Control Problems ◽

Element Approximation ◽

Navier Stokes Equations ◽

Stationary Navier Stokes Equations

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Maximum Principle for Some Optimal Control Problems Governed by 2D Nonlocal Cahn–Hillard–Navier–Stokes Equations

Journal of Mathematical Fluid Mechanics ◽

10.1007/s00021-020-00493-8 ◽

2020 ◽

Vol 22 (3) ◽

Author(s):

Tania Biswas ◽

Sheetal Dharmatti ◽

Manil T. Mohan

Keyword(s):

Optimal Control ◽

Maximum Principle ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Control Problems ◽

Navier Stokes Equations

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Analysis of the SQP-Method for Optimal Control Problems Governed by the Nonstationary Navier–Stokes Equations Based on $L^p$-theory

SIAM Journal on Control and Optimization ◽

10.1137/s0363012904443506 ◽

2007 ◽

Vol 46 (3) ◽

pp. 1133-1153 ◽

Author(s):

Daniel Wachsmuth

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Control Problems ◽

Navier Stokes Equations

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A parallel stabilized finite element variational multiscale method based on fully overlapping domain decomposition for the incompressible Navier-Stokes equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.09.001 ◽

2021 ◽

Vol 159 ◽

pp. 138-158

Author(s):

Bo Zheng ◽

Yueqiang Shang

Keyword(s):

Finite Element ◽

Domain Decomposition ◽

Stokes Equations ◽

Multiscale Method ◽

Navier Stokes ◽

Variational Multiscale Method ◽

Navier Stokes Equations ◽

Stabilized Finite Element ◽

Variational Multiscale ◽

Overlapping Domain Decomposition

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A two-level fully discrete finite element variational multiscale method for the unsteady Navier–Stokes equations

Computational and Applied Mathematics ◽

10.1007/s40314-019-0798-4 ◽

2019 ◽

Vol 38 (2) ◽

Author(s):

Jufeng Xue ◽

Yueqiang Shang

Keyword(s):

Finite Element ◽

Stokes Equations ◽

Multiscale Method ◽

Navier Stokes ◽

Variational Multiscale Method ◽

Navier Stokes Equations ◽

Variational Multiscale ◽

Fully Discrete ◽

Discrete Finite Element

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Differential Stability of Control-Constrained Optimal Control Problems for the Navier-Stokes Equations

Numerical Functional Analysis and Optimization ◽

10.1080/01630560500434278 ◽

2005 ◽

Vol 26 (7-8) ◽

pp. 829-850 ◽

Author(s):

Roland Griesse ◽

Michael Hintermüller ◽

Michael Hinze

Keyword(s):

Optimal Control ◽

Optimal Control Problems ◽

Stokes Equations ◽

Navier Stokes ◽

Control Problems ◽

Navier Stokes Equations ◽

Constrained Optimal Control ◽

Differential Stability

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