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AIMS Mathematics

2022, Volume 7, Issue 9: 17461-17474. doi: 10.3934/math.2022962
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Research article

Multipoint flux mixed finite element method for parabolic optimal control problems

  • 1.
    School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, Shandong, China
  • 2.
    College of Information Science and Engineering, Shandong Agricultural University, Taian 271018, Shandong, China
  • Received: 01 May 2022 Revised: 17 July 2022 Accepted: 22 July 2022 Published: 28 July 2022

  • MSC : 65N12, 65N15

  • In this paper, we research semi-discrete multipoint flux mixed finite element (MFMFE) method for parabolic optimal control problem (OCP). The state and co-state variables are approximated by the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element (MFE) spaces and the control is approximated by piecewise constant. The advantage of this type of mixed element method is that it can decouple the state and adjoint state variables as cell-centered difference schemes rather than to solve saddle point algebraic equations. Error estimates and convergence orders are derived rigorously for state and control variables. Finally, a numerical example is given to confirm our theoretical analysis.

    Citation: Tiantian Zhang, Wenwen Xu, Xindong Li, Yan Wang. Multipoint flux mixed finite element method for parabolic optimal control problems[J]. AIMS Mathematics, 2022, 7(9): 17461-17474. doi: 10.3934/math.2022962

    Related Papers:

  • In this paper, we research semi-discrete multipoint flux mixed finite element (MFMFE) method for parabolic optimal control problem (OCP). The state and co-state variables are approximated by the lowest order Brezzi-Douglas-Marini (BDM) mixed finite element (MFE) spaces and the control is approximated by piecewise constant. The advantage of this type of mixed element method is that it can decouple the state and adjoint state variables as cell-centered difference schemes rather than to solve saddle point algebraic equations. Error estimates and convergence orders are derived rigorously for state and control variables. Finally, a numerical example is given to confirm our theoretical analysis.


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