A discontinuous Galerkin method for optimal control problems governed by a system of convection–diffusion PDEs with nonlinear reaction terms. (November 2015)

• Record Type: Journal Article
• Authors: Yücel, Hamdullah; Stoll, Martin; Benner, Peter
• Is Part Of: Computers & mathematics with applications. Volume 70:issue 10(2015)
• Page Start: 2414
• Page End: 2431
• Publication Date: 2015-11
• Subjects: Optimal control problem -- Convection dominated equation -- Discontinuous Galerkin method -- A posteriori error estimate -- Preconditioning; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.09.006
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, we study the numerical solution of optimal control problems governed by a system of convection–diffusion PDEs with nonlinear reaction terms, arising from chemical processes. The symmetric interior penalty Galerkin (SIPG) method with upwinding for the convection term is used as a discretization method. We use a residual-based error estimator for the state and the adjoint variables. An adaptive mesh refinement indicated by a posteriori error estimates is applied. The arising saddle point system is solved using a suitable preconditioner. Numerical results are presented to illustrate the performance of the proposed error estimator.