Publication Results

Code: MOX 69
Title: Numerical Approximation of a Control Problem for Advection-Diffusion Processes
Date: Tuesday 27th September 2005
Author(s) : Quarteroni, A.; Rozza, G.; Dede', L.; Quaini, A.
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Abstract: Two 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 Galerkin-Finite Element (FE) method, we adopt a novel a posteriori error estimate of the discretization error in the cost functional this estimated 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.