A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms

Yuecel H., STOLL M., BENNER P.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, cilt.70, sa.10, ss.2414-2431, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 70 Sayı: 10
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1016/j.camwa.2015.09.006
  • Dergi Adı: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2414-2431
  • Anahtar Kelimeler: Optimal control problem, Convection dominated equation, Discontinuous Galerkin method, A posteriori error estimate, Preconditioning, FINITE-ELEMENT METHODS, OPTIMAL BOUNDARY CONTROL, ELLIPTIC PROBLEMS, CONTROL CONSTRAINTS, REACTION EQUATIONS, LINEAR-SYSTEMS, ERROR ANALYSIS, APPROXIMATION, ALGORITHM
  • Orta Doğu Teknik Üniversitesi Adresli: Hayır

Özet

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. (C) 2015 Elsevier Ltd. All rights reserved.