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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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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.