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 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. © 2006 International Federation for Information Processing.
CITATION STYLE
Quarteroni, A., Rozza, G., Dedè, L., & Quaini, A. (2006). Numerical approximation of a control problem for advection-diffusion processes. IFIP International Federation for Information Processing, 199, 261–273. https://doi.org/10.1007/0-387-33006-2_24
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