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

Date

2015-09-01

Author

Yücel, Hamdullah

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

162
views

0
downloads

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

Suggestions

OpenMETU
Core

Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equations Stoll, Martin; Yücel, Hamdullah; Benner, Peter (2018-01-01) In this paper, we investigate a posteriori error estimates of a control-constrained optimal control problem governed by a time-dependent convection diffusion equation. The control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method and by adding a Moreau-Yosida-type penalty function to the cost functional. Residual-based error estimators are proposed for both approaches. The derived error estimators are used as error indicators to guide the mesh refinements. ...
Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints Yücel, Hamdullah; Karasözen, Bülent (2014-01-02) In this paper, we study a posteriori error estimates of the upwind symmetric interior penalty Galerkin (SIPG) method for the control constrained optimal control problems governed by linear diffusion-convection-reaction partial differential equations. Residual based error estimators are used for the state, the adjoint and the control. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented for convection dominated problems to illustrate the theoretic...
Distributed Optimal Control Problems Governed by Coupled Convection Dominated PDEs with Control Constraints Yücel, Hamdullah (2013-08-30) We study the numerical solution of control constrained optimal control problems governed by a system of convection diffusion equations with nonlinear reaction terms, arising from chemical processes. Control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method or by adding a Moreau-Yosida-type penalty function to the cost functional. An adaptive mesh refinement indicated by a posteriori error estimates is applied for both approaches.
A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms Yücel, Hamdullah; BENNER, Peter (2015-11-01) In this paper, we study the numerical solution of optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms, arising from chemical processes. The symmetric interior penalty Galerkin (SIPG) method with upwinding for the convection term is used as a discretization method. We use a residual-based error estimator for the state and the adjoint variables. An adaptive mesh refinement indicated by a posteriori error estimates is applied. The arising saddle point system...
Goal–oriented a posteriori error estimation for Dirichlet boundary control problems Yücel, Hamdullah (Elsevier BV, 2021-1) We study goal-oriented a posteriori error estimates for the numerical approximation ofDirichlet boundary control problem governed by a convection diffusion equation withpointwise control constraints on a two dimensional convex polygonal domain. The localdiscontinuous Galerkin method is used as a discretization technique since the controlvariable is involved in a variational form in a natural sense. We derive primal–dualweightederrorestimatesfortheobjectivefunctionalwithanerrortermrepresentingthemismatch in ...

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.