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


Yuecel H. , BENNER P.

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, cilt.62, ss.291-321, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 62 Konu: 1
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s10589-014-9691-7
  • Dergi Adı: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • Sayfa Sayıları: ss.291-321

Özet

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.