Year: 2023
Author: Jiaqi Zhang, Yin Yang, Zhaojie Zhou
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 6 : pp. 1631–1654
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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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0173
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 6 : pp. 1631–1654
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Fractional Laplacian optimal control problem Caffarelli-Silvestre extension weighted Laguerre polynomials.