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, vol.70, no.10, pp.2414-2431, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 70 Issue: 10
  • Publication Date: 2015
  • Doi Number: 10.1016/j.camwa.2015.09.006
  • Title of Journal : COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Page Numbers: pp.2414-2431
  • Keywords: 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

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