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AIMS Mathematics

2021, Volume 6, Issue 1: 979-997. doi: 10.3934/math.2021059
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Research article

Finite element approximation of time fractional optimal control problem with integral state constraint

  • School of Mathematics and Statistics, Shandong Normal University
  • Received: 13 September 2020 Accepted: 27 October 2020 Published: 05 November 2020

  • MSC : 65K10, 65N30

  • In this paper we investigate the finite element approximation of time fractional optimal control problem with integral state constraint. A space-time finite element scheme for the control problem is developed with piecewise constant time discretization and piecewise linear spatial discretization for the state equation. A priori error estimate for the space-time discrete scheme is derived. Projected gradient algorithm is used to solve the discrete optimal control problem. Numerical experiments are carried out to illustrate the theoretical findings.

    Citation: Jie Liu, Zhaojie Zhou. Finite element approximation of time fractional optimal control problem with integral state constraint[J]. AIMS Mathematics, 2021, 6(1): 979-997. doi: 10.3934/math.2021059

    Related Papers:

  • In this paper we investigate the finite element approximation of time fractional optimal control problem with integral state constraint. A space-time finite element scheme for the control problem is developed with piecewise constant time discretization and piecewise linear spatial discretization for the state equation. A priori error estimate for the space-time discrete scheme is derived. Projected gradient algorithm is used to solve the discrete optimal control problem. Numerical experiments are carried out to illustrate the theoretical findings.


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