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

2014-05-01
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.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

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Citation Formats
Z. K. Seymen, H. Yücel, and B. Karasözen, “Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 146–157, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32525.