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

Date

2015-11-01

Author

Yücel, Hamdullah
BENNER, Peter

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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 is solved using a suitable preconditioner. Numerical results are presented to illustrate the performance of the proposed error estimator.

Subject Keywords

Preconditioning, A posteriori error estimate, Discontinuous Galerkin method, Convection dominated equation, Optimal control problem

URI

https://hdl.handle.net/11511/30908

Journal

COMPUTERS & MATHEMATICS WITH APPLICATIONS

DOI

https://doi.org/10.1016/j.camwa.2015.09.006

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

H. Yücel and P. BENNER, “A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 2414–2431, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30908.