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Research Article | Open Access

Superconvergence for optimal control problems governed by semilinear parabolic equations

Chunjuan Hou1, Zuliang Lu2,3( ), Xuejiao Chen1, Xiankui Wu2, Fei Cai2
Department of Data Science, Guangzhou Huashang College, Guangzhou 511300, China
Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges University, Chongqing, 404000, China
Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin, 300222, China
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Abstract

In this paper, we first investigate optimal control problem for semilinear parabolic and introduce the standard L 2 ( Ω )-orthogonal projection and the elliptic projection. Then we present some necessary intermediate variables and their error estimates. At last, we derive the error estimates between the finite element solutions and L 2 -orthogonal projection or the elliptic projection of the exact solutions.

Keywords

finite element approximationsemilinear parabolic equationoptimal control problemthe elliptic projectionL2-orthogonal projectionsuperconvergence
CLC number: 49J20, 65N30

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 9405-9423
DOI: 10.3934/math.2022522

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Cite this article:
Hou C, Lu Z, Chen X, et al. Superconvergence for optimal control problems governed by semilinear parabolic equations. AIMS Mathematics, 2022, 7(5): 9405-9423. https://doi.org/10.3934/math.2022522

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Received: 08 October 2021
Revised: 03 February 2022
Accepted: 28 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)