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

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.