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

2015-09-01
Yücel, Hamdullah
BENNER, Peter
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.

Citation Formats
H. Yücel and P. BENNER, “Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations,” COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, vol. 62, no. 1, pp. 291–321, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32457.