An Adaptive POD Approximation Method for the Control of Advection-Diffusion Equations
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.
KeywordsOptimal Control Proper orthogonal decomposition Hamilton–Jacobi equations Advection-diffusion equations
Mathematics Subject Classification (2010)49J20 49L20 49M25
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