Error estimates for the approximation of the velocity tracking problem with Bang-Bang controls

Abstract: 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 suffcient 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, t and h respectively, satisfy t_> Ch2 , then L2 error estimates are proved for the difference between the states corresponding to locally optimal controls and their discrete approximations.

 Autoría: Casas E., Chrysafinos K.,

 Fuente: ESAIM: Control, Optimisation and Calculus of Variations, 2017, 23(4), 1267-1291

Editorial: EDP Sciences

 Fecha de publicación: 01/10/2017

Nº de páginas: 25

Tipo de publicación: Artículo de Revista

DOI: 10.1051/cocv/2016054

ISSN: 1292-8119,1262-3377

Proyecto español: MTM2011- 22711 ; MTM2014-57531-P

Url de la publicación: https://doi.org/10.1051/cocv/2016054