TY - JOUR
T1 - Finite Element Approximation of Space Fractional Optimal Control Problem with Integral State Constraint
AU - Zhou , Zhaojie
AU - Song , Jiabin
AU - Chen , Yanping
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1027
EP - 1049
PY - 2020
DA - 2020/06
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0201
UR - https://global-sci.org/intro/article_detail/nmtma/16965.html
KW - Finite element method, optimal control problem, state constraint, space fractional
equation, a priori error estimate, fast algorithm.
AB - <p style="text-align: justify;">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.</p>