Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints
Date
2014-01-02
Author
Yücel, Hamdullah
Karasözen, Bülent
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
206
views
0
downloads
Cite This
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 theoretical findings and the effectiveness of the adaptivity.
Subject Keywords
A posteriori error estimates
,
Discontinuous Galerkin method
,
Convection dominated equations
,
Control constraints
,
Optimal control problems
URI
https://hdl.handle.net/11511/30650
Journal
OPTIMIZATION
DOI
https://doi.org/10.1080/02331934.2013.801474
Collections
Graduate School of Applied Mathematics, Article
Suggestions
OpenMETU
Core
Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations
Yücel, Hamdullah (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 poste...
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 METHOD FOR BOUNDARY CONTROL PROBLEMS
BENNER, Peter; Yücel, Hamdullah (2017-01-01)
We investigate an a posteriori error analysis of adaptive finite element approximations of linear-quadratic boundary optimal control problems under bilateral box constraints, which act on a Neumann boundary control. We use a symmetric interior Galerkin method as discretization technique. An efficient and reliable residual-type error estimator is introduced by invoking data oscillations. We then derive local upper and lower a posteriori error estimates for the boundary control problem. Adaptive mesh refineme...
A priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equations
AKMAN, Tugba; Yücel, Hamdullah; Karasözen, Bülent (2014-04-01)
In this paper, we analyze the symmetric interior penalty Galerkin (SIPG) for distributed optimal control problems governed by unsteady convection diffusion equations with control constraint bounds. A priori error estimates are derived for the semi- and fully-discrete schemes by using piecewise linear functions. Numerical results are presented, which verify the theoretical results.
Distributed Optimal Control of Diffusion Convection Reaction Equations Using Discontinuous Galerkin Methods
Yücel, Hamdullah; Karasözen, Bülent (2011-09-09)
We discuss the symmetric interior penalty Galerkin (SIPG) method, the nonsymmetric interior penalty Galerkin (NIPG) method, and the incomplete interior penalty Galerkin (IIPG) method for the discretization of optimal control problems governed by linear diffusion-convection-reaction equations. For the SIPG discretization the discretize-then-optimize (DO) and the optimize-then-discretize (OD) approach lead to the same discrete systems and in both approaches the observed L 2 convergence for states and controls...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
H. Yücel and B. Karasözen, “Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints,”
OPTIMIZATION
, pp. 145–166, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30650.