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Journal of Applied Mathematics and Computing

Erschienen in:

12.12.2023 | Original Research

An iterative proper orthogonal decomposition method for a parabolic optimal control problem

verfasst von: Liuping Huang, Hai Zhao, Tongjun Sun

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1/2024

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Abstract

An iterative proper orthogonal decomposition (POD) method for a parabolic optimal control problem is investigated in this paper. Firstly, we construct the finite element method, where piecewise linear continuous functions are used for space discretization, and the backward Euler method is used for time discretization. Secondly, we apply the POD method as a model order reduction method to reduce the computation. The different POD basis functions for the state and co-state variables are established by an iterative procedure, which takes the finite element solutions at some time instances as snapshots. A priori error estimates are derived for the state, co-state and control variables, respectively. Finally, numerical experiments are provided to support our theoretical results.

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Titel: An iterative proper orthogonal decomposition method for a parabolic optimal control problem
verfasst von: Liuping Huang
Hai Zhao
Tongjun Sun
Publikationsdatum: 12.12.2023
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1/2024
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-023-01961-w

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