Unsteady optimal control problems arising from chemical processes

Yücel, Hamdullah
Benner, Peter
This talk will focus on the numerical solution of unsteady optimal control problems governed by a system of convection diffusion partial differential equations (PDEs) with nonlinear reaction terms arising from chemical processes. Such problems are strongly coupled as inaccuracies in one unknown directly affect all other unknowns. Prediction of these unknowns is very important for the safe and economical operation of biochemical and chemical engineering processes. Further, the solutions of these PDEs can exhibit layers on small regions where the solution has large gradients, when convection dominates diffusion. To avoid spurious oscillations emerging from the layers, we use adaptive mesh refinement. The symmetric interior penalty Galerkin (SIPG) method with upwinding for the convection term is used for space discretization, whereas backward Euler is used for time discretization. Residual-based error estimators are used for the state, the adjoint and the control variables. 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.


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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...
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Citation Formats
H. Yücel and P. Benner, “Unsteady optimal control problems arising from chemical processes,” presented at the ESCO 2014, 4th European Seminar on Computing (15 - 20 Haziran 2014), Pilsen, Çek Cumhuriyeti, 2014, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/85499.