Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:261

Article

Seymen, Z. Kanar¹  Yucel, H.^1,2  Karasozen, B.^1,2 

[1] Middle E Tech Univ, Dept Math, TR-06800 Ankara, Turkey

[2] Middle E Tech Univ, Inst Appl Math, TR-06800 Ankara, Turkey

关键词: Optimal control problems;    Stabilized finite elements;    Convection dominated problems;    Pointwise inequality constraints;    COMSOL Multiphysics;   

DOI  :  10.1016/j.cam.2013.11.006

来源: Elsevier

【 摘 要 】

We apply two different strategies for solving unsteady distributed optimal control problems governed by diffusion-convection-reaction equations. In the first approach, the optimality system is transformed into a biharmonic equation in the space time domain. The system is then discretized in space and time simultaneously and solved by an equation-based finite element package, i.e., COMSOL Multiphysics. The second approach is a classical gradient-based optimization method to solve the state and adjoint equations and the optimality condition iteratively. The convection-dominated state and adjoint equations are stabilized using the streamline upwind/Petrov-Galerkin (SUPG) method. Numerical results show favorable accuracy and efficiency of the two strategies for unstabilized and stabilized numerical solutions. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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