Numerical solutions for optimal control problem governed by elliptic system on Lipschitz domains. Issue 1 (11th December 2019)

• Record Type: Journal Article
• Authors: Bahaa, G. M.; Khidr, S.
• Is Part Of: Journal of Taibah University for science. Volume 13:Issue 1(2019)
• Page Start: 41
• Page End: 48
• Publication Date: 2019-12-11
• Subjects: Optimal control problem -- elliptic system -- Dirichlet and Neumann boundary conditions -- Sobolev spaces on Lipschitz domains -- Jacobi polynomials -- spectral Galerkin method; 46C05 -- 49J20 -- 93C20; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2018.1522739
• Languages: English
• ISSNs: 1658-3655

Abstract

ABSTRACT: In this paper, an optimal boundary control problem for a distributed elliptic system on Lipschitz domains with boundary homogeneous Dirichlet conditions and independently with Neumann conditions is analysed. The necessary and sufficient optimality conditions for such problems with the quadratic cost functionals are obtained. A Jacobi spectral Galerkin method is introduced to develop a direct solution technique for the numerical solution of elliptic problems subject to Dirichlet and Neumann conditions in one and two dimensions. The numerical examples are included to demonstrate the validity and applicability of the techniques and comparison is made with the existing results. The method is easy to implement and yields very accurate results.