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

Date

2015-09-01

Author

Yücel, Hamdullah

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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.

Subject Keywords

Optimal Control Problem, State Constraints, Discontinuous Galerkin Methods, Convection Diffusion Equations, A Posteriori Error Estimates

URI

https://hdl.handle.net/11511/32457

Journal

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS

DOI

https://doi.org/10.1007/s10589-014-9691-7

Collections

Graduate School of Applied Mathematics, Article

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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.