Numerical approximation of a control problem for advection-diffusion processes

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.


Published in:
System modeling and optimization, 199, 261-273
Year:
2006
Publisher:
Boston, Springer
Keywords:
Laboratories:




 Record created 2007-04-24, last modified 2018-03-17


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