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

2015-09-01
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.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

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Citation Formats
H. Yücel, “Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations,” COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, pp. 291–321, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32457.