Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint

Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint

Year:    2020

Author:    Yanping Chen, Zhaojie Zhou, Jiabin Song, Yanping Chen

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 1027–1049

Abstract

In this paper finite element approximation of space fractional optimal control problem with integral state constraint is investigated. First order optimal condition and regularity of the control problem are discussed. A priori error estimates for control, state, adjoint state and lagrange multiplier are derived. The nonlocal property of the fractional derivative results in a dense coefficient matrix of the discrete state and adjoint state equation. To reduce the computational cost a fast projection gradient algorithm is developed based on the Toeplitz structure of the coefficient matrix. Numerical experiments are carried out to illustrate the theoretical findings.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2019-0201

Numerical Mathematics: Theory, Methods and Applications, Vol. 13 (2020), Iss. 4 : pp. 1027–1049

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Finite element method optimal control problem state constraint space fractional equation a priori error estimate fast algorithm.

Author Details

Yanping Chen

Zhaojie Zhou

Jiabin Song

Yanping Chen