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

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• 作者：Hamdullah Yü ; cel ; ^{yuecel@mpi-magdeburg.mpg.de" class="auth_mail" title="E-mail the corresponding author} ; Martin Stoll ^{stollm@mpi-magdeburg.mpg.de" class="auth_mail" title="E-mail the corresponding author} ; Peter Benner ^{benner@mpi-magdeburg.mpg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Optimal control problem ; Convection dominated equation ; Discontinuous Galerkin method ; A posteriori error estimate ; Preconditioning
• 刊名：Computers & Mathematics with Applications
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：70
• 期：10
• 页码：2414-2431
• 全文大小：1201 K

文摘

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.