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

• Autores: Z. Kanar Seymen, H. Yücel, Bülent Karasözen
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 261, Nº 1, 2014, págs. 146-157
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.11.006
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• Resumen

  • 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 equationbased 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.