Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations

Yuecel H., BENNER P.

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, vol.62, no.1, pp.291-321, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.1007/s10589-014-9691-7
  • Journal Name: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.291-321
  • Keywords: Optimal control problem, State constraints, Discontinuous Galerkin methods, Convection diffusion equations, A posteriori error estimates, ELLIPTIC CONTROL-PROBLEMS, FINITE-ELEMENT METHODS, POSTERIORI ERROR ESTIMATION, LAGRANGE MULTIPLIERS, APPROXIMATION, STRATEGY
  • Middle East Technical University Affiliated: No

Abstract

We study a posteriori error estimates for the numerical approximations of state constrained optimal control problems governed by convection diffusion equations, regularized by Moreau-Yosida and Lavrentiev-based techniques. The upwind Symmetric Interior Penalty Galerkin (SIPG) method is used as a discontinuous Galerkin (DG) discretization method. We derive different residual-based error indicators for each regularization technique due to the regularity issues. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented to illustrate the effectiveness of the adaptivity for both regularization techniques.