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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.
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https://hal.inria.fr/hal-00800433
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, March 13, 2013 - 4:23:37 PM
Last modification on : Wednesday, July 27, 2016 - 2:48:48 PM

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  • HAL Id : hal-00800433, version 1
  • ARXIV : 1302.4072

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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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