AIMS Mathematics

2022, Issue 5: 9405-9423. doi: 10.3934/math.2022522
Research article Special Issues

Superconvergence for optimal control problems governed by semilinear parabolic equations

• Received: 08 October 2021 Revised: 03 February 2022 Accepted: 28 February 2022 Published: 11 March 2022
• MSC : 49J20, 65N30

• In this paper, we first investigate optimal control problem for semilinear parabolic and introduce the standard $L^2(\Omega)$-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.

Citation: Chunjuan Hou, Zuliang Lu, Xuejiao Chen, Xiankui Wu, Fei Cai. Superconvergence for optimal control problems governed by semilinear parabolic equations[J]. AIMS Mathematics, 2022, 7(5): 9405-9423. doi: 10.3934/math.2022522

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• In this paper, we first investigate optimal control problem for semilinear parabolic and introduce the standard $L^2(\Omega)$-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.

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