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A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem

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Abstract

In this paper, a virtual element method (VEM) discretization of elliptic optimal control problem with pointwise control constraint is investigated. Virtual element discrete scheme is constructed based on virtual element approximation of the state equation and variational discretization of the control variable. A priori error estimates for state, adjoint state and control variable in H1 and L2 norms are derived. Due to the attractive flexibility of VEM in dealing with mesh refinement we also derive a posteriori error estimates for the optimal control problem, which are used to guide the mesh refinement in the adaptive VEM algorithm. Numerical experiments are carried out to illustrate the theoretical findings.

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  • 02 February 2022

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Funding

The research was supported by the NSFC of China (No. 11971276,11301311) and the NSFC of Shandong Province (No. ZR2016JL004, No. ZR2021MA049).

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  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Qiming Wang & Zhaojie Zhou

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  1. Qiming Wang
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  2. Zhaojie Zhou
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Correspondence to Zhaojie Zhou.

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Wang, Q., Zhou, Z. A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem. Numer Algor 90, 989–1015 (2022). https://doi.org/10.1007/s11075-021-01219-1

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