A One Dimensional Elliptic Distributed Optimal Control Problem with Pointwise Derivative Constraints. (2nd October 2020)

• Record Type: Journal Article
• Authors: Brenner, Susanne C.; Sung, Li-yeng; Wollner, Winnifried
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 13(2020)
• Page Start: 1549
• Page End: 1563
• Publication Date: 2020-10-02
• Subjects: Cubic Hermite element -- Dirichlet boundary condition -- elliptic distributed optimal control problem -- One dimensional -- pointwise derivative constraints; 49J15 -- 65N30 -- 65N15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1785495
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain higher regularity for the optimal state under appropriate assumptions on the data. We also solve the optimal control problem as a fourth order variational inequality by a C 1 finite element method, and present the error analysis together with numerical results.