This paper is concerned with the analysis of the finite element approximations of Dirichlet control problem using boundary penalty method for unsteady Navier–Stokes equations. Boundary penalty method has been used as a computationally convenient approach alternative to Dirichlet boundary control problems governed by Navier−Stokes equations due to its variational properties. Analysis of the mixed Galerkin finite element method applied to the spatial semi-discretization of the optimality system, from which optimal control can be computed, is presented. An optimal error estimate of the numerical approximations of the optimality system is derived. Feasibility and applicability of the approach are illustrated by numerically solving a canonical flow control problem.
Accepté le :
DOI : 10.1051/m2an/2016040
Mots clés : Boundary penalty method, Dirichlet boundary control, Navier–Stokes equations, optimal error estimates, mixed Galerkin finite element, adjoint equations
@article{M2AN_2017__51_3_825_0,
author = {Ravindran, Sivaguru S.},
title = {Finite element approximation of {Dirichlet} control using boundary penalty method for unsteady {Navier{\textendash}Stokes} equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {825--849},
publisher = {EDP-Sciences},
volume = {51},
number = {3},
year = {2017},
doi = {10.1051/m2an/2016040},
mrnumber = {3666648},
zbl = {1457.65133},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2016040/}
}
TY - JOUR AU - Ravindran, Sivaguru S. TI - Finite element approximation of Dirichlet control using boundary penalty method for unsteady Navier–Stokes equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 825 EP - 849 VL - 51 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2016040/ DO - 10.1051/m2an/2016040 LA - en ID - M2AN_2017__51_3_825_0 ER -
%0 Journal Article %A Ravindran, Sivaguru S. %T Finite element approximation of Dirichlet control using boundary penalty method for unsteady Navier–Stokes equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 825-849 %V 51 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2016040/ %R 10.1051/m2an/2016040 %G en %F M2AN_2017__51_3_825_0
Ravindran, Sivaguru S. Finite element approximation of Dirichlet control using boundary penalty method for unsteady Navier–Stokes equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 825-849. doi : 10.1051/m2an/2016040. http://archive.numdam.org/articles/10.1051/m2an/2016040/
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