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Reduced-order finite element approximation based on POD for the parabolic optimal control problem

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Abstract

In this paper, we construct a reduced-order finite element (ROFE) method holding seldom unknowns for the parabolic optimal control problem. We apply the proper orthogonal decomposition (POD) technique to develop two unsteady systems about state and co-state approximations, which efficiently reduces the number of unknowns and computational costs. Optimal a priori error estimates for the state, co-state and control approximations are derived. Finally, numerical examples are presented to verify that the ROFE method is accurate and efficient for solving the parabolic optimal control problem.

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Funding

The work is supported by the National Natural Science Foundation of China Grant No. 12201354, 12131014 and the Postdoctoral Innovation Project of Shandong Province Grant No. SDCX-ZG-202202017.

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  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Junpeng Song & Hongxing Rui

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  1. Junpeng Song
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Correspondence to Hongxing Rui.

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Song, J., Rui, H. Reduced-order finite element approximation based on POD for the parabolic optimal control problem. Numer Algor 95, 1189–1211 (2024). https://doi.org/10.1007/s11075-023-01605-x

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