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arXiv · 1302.4072

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

Alessandro Alla·Maurizio Falcone
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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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Alessandro Alla, Maurizio Falcone. 2013-02-17. An adaptive POD approximation method for the control of advection-diffusion equations. https://arxiv.org/abs/1302.4072

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