Distributed optimal control of time-dependent diffusion-convection-reaction equations using space-time discretization
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.261, pp.146-157, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 261
- Publication Date: 2014
- Doi Number: 10.1016/j.cam.2013.11.006
- Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.146-157
- Keywords: Optimal control problems, Stabilized finite elements, Convection dominated problems, Pointwise inequality constraints, COMSOL Multiphysics, FINITE-ELEMENT METHODS, MESH-INDEPENDENCE, ERROR ANALYSIS, A-PRIORI, STABILIZATION
- Middle East Technical University Affiliated: Yes
Abstract
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.