scholarly journals Multigrid Preconditioners for the Newton--Krylov Method in the Optimal Control of the Stationary Navier--Stokes Equations

2019 ◽  
Vol 57 (3) ◽  
pp. 1494-1523
Author(s):  
Ana Maria Soane ◽  
Andrei Drăgănescu
Keyword(s):  
Optimal Control ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Krylov Method ◽  
Stationary Navier Stokes Equations ◽  
Multigrid Preconditioners

Numerical resolution of optimal control problem for the in-stationary Navier–Stokes equations

2019 ◽  
Vol 27 (1) ◽  
pp. 43-52
Author(s):  
Jamil Satouri
Keyword(s):  
Optimal Control ◽  
Finite Elements ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stokes Equations ◽  
Explicit Scheme ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Resolution ◽  
Stationary Navier Stokes Equations

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. Finally, we give some numerical results proving the effectiveness of our approach.

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