Quarteroni, AlfioRozza, GianluigiDede', LucaQuaini, Annalisa2007-04-242007-04-242007-04-24200610.1007/0-387-33006-2_24https://infoscience.epfl.ch/handle/20.500.14299/5441WOS:000236895000024Two different approaches are proposed to enhance the efficiency of the numerical resolution of optimal control problems governed by a linear advection-diffusion equation. In the framework of the Galerkin-Finite Element (FE) method, we adopt a novel a posteriori error estimate of the discretization error on the cost functional; this estimate is used in the course of a numerical adaptive strategy for the generation of efficient grids for the resolution of the optimal control problem. Moreover, we propose to solve the control problem by adopting a reduced basis (RB) technique, hence ensuring rapid, reliable and repeated evaluations of input-output relationship. Our numerical tests show that by this technique a substantial saving of computational costs can be achieved.optimal control problemspartial differential equationsfinite element approximationreduced basis techniquesadvection-diffusion equationsstabilized Lagrangiannumerical adaptivitytext::book/monograph::book part or chapter