A discontinous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms / Hamdullah Yücel, Martin Stoll, Peter Benner

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 for discretization. Residual-based error estimators are used for the state, the adjoint and the control 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 examples are presented for convection dominated problems to illustrate the effectiveness of the adaptivity.