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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

    Related Papers:

  • 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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