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Book Sections Year : 2013

An adaptive POD approximation method for the control of advection-diffusion equations

Abstract

We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic Programming approximation scheme for the corresponding evolutive Hamilton-Jacobi equation. We discuss several features regarding the adaptivity of the method, the role of error estimate indicators to choose a time subdivision of the problem and the computation of the basis functions. Some test problems are presented to illustrate the method.

Dates and versions

hal-00800433 , version 1 (13-03-2013)

Identifiers

Cite

Alessandro Alla, Maurizio Falcone. An adaptive POD approximation method for the control of advection-diffusion equations. Bredies, K.; Clason, C.; Kunisch, K.; von Winckel, G. Control and Optimization with PDE Constraints, 164, Springer, 2013, International Series of Numerical Mathematics,, 978-3-0348-0630-5. ⟨hal-00800433⟩
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