The velocity tracking problem for the evolutionary Navier–Stokes equations in 2d is studied. The controls are of distributed type but the cost functional does not involve the usual quadratic term for the control. As a consequence the resulting controls can be of bang-bang type. First and second order necessary and sufficient conditions are proved. A fully-discrete scheme based on discontinuous (in time) Galerkin approach combined with conforming finite element subspaces in space, is proposed and analyzed. Provided that the time and space discretization parameters, and respectively, satisfy , then error estimates are proved for the difference between the states corresponding to locally optimal controls and their discrete approximations.
Accepted:
DOI: 10.1051/cocv/2016054
Keywords: Evolution Navier–Stokes equations, optimal control, bang-bang controls, a priori error estimates
@article{COCV_2017__23_4_1267_0, author = {Casas, Eduardo and Chrysafinos, Konstantinos}, title = {Error estimates for the approximation of the velocity tracking problem with {Bang-Bang} controls}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1267--1291}, publisher = {EDP-Sciences}, volume = {23}, number = {4}, year = {2017}, doi = {10.1051/cocv/2016054}, zbl = {1388.49003}, mrnumber = {3716921}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016054/} }
TY - JOUR AU - Casas, Eduardo AU - Chrysafinos, Konstantinos TI - Error estimates for the approximation of the velocity tracking problem with Bang-Bang controls JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 1267 EP - 1291 VL - 23 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016054/ DO - 10.1051/cocv/2016054 LA - en ID - COCV_2017__23_4_1267_0 ER -
%0 Journal Article %A Casas, Eduardo %A Chrysafinos, Konstantinos %T Error estimates for the approximation of the velocity tracking problem with Bang-Bang controls %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 1267-1291 %V 23 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016054/ %R 10.1051/cocv/2016054 %G en %F COCV_2017__23_4_1267_0
Casas, Eduardo; Chrysafinos, Konstantinos. Error estimates for the approximation of the velocity tracking problem with Bang-Bang controls. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 4, pp. 1267-1291. doi : 10.1051/cocv/2016054. http://archive.numdam.org/articles/10.1051/cocv/2016054/
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