TY - JOUR
T1 - Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian
AU - Zhang , Jiaqi
AU - Yang , Yin
AU - Zhou , Zhaojie
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1631
EP - 1654
PY - 2023
DA - 2023/10
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2022-0173
UR - https://global-sci.org/intro/article_detail/aamm/22054.html
KW - Fractional Laplacian, optimal control problem, Caffarelli-Silvestre extension, weighted Laguerre polynomials.
AB - <p style="text-align: justify;">In this paper spectral Galerkin approximation of optimal control problem
governed by fractional elliptic equation is investigated. To deal with the nonlocality
of fractional Laplacian operator the Caffarelli-Silvestre extension is utilized. The first
order optimality condition of the extended optimal control problem is derived. A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre
polynomials is developed. A priori error estimates for the spectral Galerkin discrete
scheme is proved. Numerical experiments are presented to show the effectiveness of
our methods and to verify the theoretical findings.</p>