Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints


Yucel H. , Karasozen B.

OPTIMIZATION, vol.63, no.1, pp.145-166, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 1
  • Publication Date: 2014
  • Doi Number: 10.1080/02331934.2013.801474
  • Title of Journal : OPTIMIZATION
  • Page Numbers: pp.145-166
  • Keywords: optimal control problems, control constraints, convection dominated equations, discontinuous Galerkin method, a posteriori error estimates, POSTERIORI ERROR ANALYSIS, FINITE-ELEMENT METHODS

Abstract

In this paper, we study a posteriori error estimates of the upwind symmetric interior penalty Galerkin (SIPG) method for the control constrained optimal control problems governed by linear diffusion-convection-reaction partial differential equations. Residual based error estimators are used for the state, the adjoint and the control. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented for convection dominated problems to illustrate the theoretical findings and the effectiveness of the adaptivity.