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Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian
Jiaqi Zhang, Yin Yang and Zhaojie Zhou

Adv. Appl. Math. Mech. DOI: 10.4208/aamm.OA-2022-0173

Publication Date : 2023-03-13

  • Abstract

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.

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