COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, vol.62, no.1, pp.291-321, 2015 (SCI-Expanded)
Article / Article
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
Science Citation Index Expanded (SCI-EXPANDED), Scopus
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:
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.