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Analysis of the velocity tracking control problem for the 3D evolutionary navier-stokes equations

Abstract: The velocity tracking problem for the evolutionary Navier-Stokes equations in three dimensions is studied. The controls are of distributed type and are submitted to bound constraints. The classical cost functional is modified so that a full analysis of the control problem is possible. First and second order necessary and sufficient optimality conditions are proved. A fully discrete scheme based on a 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, the L2(OT) error estimates of order O(h) are proved for the difference between the locally optimal controls and their discrete approximations. Finally, combining these techniques and the approach of Casas, Herzog, and Wachsmuth [SIAM J. Optim., 22 (2012), pp. 795-820], we extend our results to the case of L1(OT) type functionals that allow sparse controls.

 Autoría: Casas E., Chrysafinos K.,

 Fuente: SIAM Journal on Control and Optimization, 2016, 54 (1), 99-128

 Editorial: Society for Industrial and Applied Mathematics

 Fecha de publicación: 01/01/2016

 Nº de páginas: 30

 Tipo de publicación: Artículo de Revista

 DOI: 10.1137/140978107

 ISSN: 0363-0129,1095-7138

 Proyecto español: MTM2011-22711