Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations

Akman T., Karasozen B.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.272, pp.41-56, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 272
  • Publication Date: 2014
  • Doi Number: 10.1016/j.cam.2014.05.002
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.41-56
  • Keywords: Optimal control problems, Unsteady diffusion-convection-reaction equation, Variational time discretization, A priori error estimates, DISCONTINUOUS GALERKIN METHODS, FINITE-ELEMENT METHODS, PARABOLIC PROBLEMS, ERROR ANALYSIS
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper, the distributed optimal control problem governed by unsteady diffusion-convection-reaction equation without control constraints is studied. Time discretization is performed by variational discretization using continuous and discontinuous Galerkin methods, while symmetric interior penalty Galerkin with upwinding is used for space discretization. We investigate the commutativity properties of the optimize-then-discretize and discretize-then-optimize approaches for the continuous and discontinuous Galerkin time discretization. A priori error estimates are derived for fully-discrete state, adjoint and control. The numerical results given for convection dominated problems via optimize-then-discretize approach confirm the theoretically observed convergence rates. (C) 2014 Elsevier B.V. All rights reserved.