An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint

被引：0

作者：

Zhang, Jiaqi ^{[1
]}

Yang, Yin ^{[2
,3
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Hunan Key Lab Computat & Simulat Sci & Engn, Key Lab Intelligent Comp & Informat Proc Minist Ed, Xiangtan, Hunan, Peoples R China

[2] Xiangtan Univ, Natl Ctr Appl Math Hunan, Sch Math & Computat Sci, Hunan Int Sci & Technol Innovat Cooperat Base Comp, Xiangtan, Hunan, Peoples R China

[3] Xiangtan Univ, Natl Ctr Appl Math Hunan, Sch Math & Computat Sci, Hunan Int Sci & Technol Innovat Cooperat Base Comp, Xiangtan 411105, Hunan, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 39卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Caffarelli-Silvestre extension; enriched spectral Galerkin method; fractional Laplacian; Laguerre polynomials; optimal control problems; FINITE-ELEMENT APPROXIMATION; ERROR ANALYSIS; CONVERGENCE; EQUATIONS; FEM;

D O I：

10.1002/num.23056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the numerical approximation of an optimal control problem with fractional Laplacian and state constraint in integral form based on the Caffarelli-Silvestre expansion. The first order optimality conditions of the extended optimal control problem is obtained. An enriched spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is proposed. A priori error estimate for the enriched spectral discrete scheme is proved. Numerical experiments demonstrate the effectiveness of our method and validate the theoretical results.

引用

页码：4403 / 4420

页数：18

共 34 条

[1] Optimal Control of Fractional Elliptic PDEs with State Constraints and Characterization of the Dual of Fractional-Order Sobolev Spaces [J].