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

Seymen Z. K., YÜCEL H., KARASÖZEN B.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.261, ss.146-157, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 261
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.cam.2013.11.006
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.146-157
  • Anahtar Kelimeler: Optimal control problems, Stabilized finite elements, Convection dominated problems, Pointwise inequality constraints, COMSOL Multiphysics, FINITE-ELEMENT METHODS, MESH-INDEPENDENCE, ERROR ANALYSIS, A-PRIORI, STABILIZATION
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.