ADAPTIVE DISCONTINUOUS GALERKIN APPROXIMATION OF OPTIMAL CONTROL PROBLEMS GOVERNED BY TRANSIENT CONVECTION-DIFFUSION EQUATIONS


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YÜCEL H. , Stoll M., Benner P.

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, vol.48, pp.407-434, 2018 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 48
  • Publication Date: 2018
  • Doi Number: 10.1553/etna_vol48s407
  • Title of Journal : ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
  • Page Numbers: pp.407-434
  • Keywords: optimal control problem, a posteriori error estimate, discontinuous Galerkin method, convection diffusion equations, FINITE-ELEMENT-METHOD, CONSTRAINED OPTIMIZATION, ERROR ANALYSIS, A-PRIORI, VARIATIONAL DISCRETIZATION, SIPG METHOD, REGULARIZATION

Abstract

In this paper, we investigate a posteriori error estimates of a control-constrained optimal control problem governed by a time-dependent convection diffusion equation. The control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method and by adding a Moreau-Yosida-type penalty function to the cost functional. Residual-based error estimators are proposed for both approaches. The derived error estimators are used as error indicators to guide the mesh refinements. A symmetric interior penalty Galerkin method in space and a backward Euler method in time are applied in order to discretize the optimization problem. Numerical results are presented, which illustrate the performance of the proposed error estimators.