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Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization
Date
2014-05-01
Author
Seymen, Z. Kanar
Yücel, Hamdullah
Karasözen, Bülent
Metadata
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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.
Subject Keywords
Optimal Control Problems
,
Stabilized Finite Elements
,
Convection Dominated Problems
,
Pointwise Inequality Constraints
,
COMSOL Multiphysics
URI
https://hdl.handle.net/11511/32525
Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
DOI
https://doi.org/10.1016/j.cam.2013.11.006
Collections
Graduate School of Applied Mathematics, Article
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BibTeX
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.