STREAMLINE UPWIND/PETROV GALERKIN SOLUTION OF OPTIMAL CONTROL PROBLEMS GOVERNED BY TIME DEPENDENT DIFFUSION-CONVECTION-REACTION EQUATIONS

2017-01-01
Akman, T.
Karasözen, Bülent
Kanar-Seymen, Z.
The streamline upwind/Petrov Galerkin (SUPG) finite element method is studied for distributed optimal control problems governed by unsteady diffusion-convection-reaction equations with control constraints. We derive stability and convergence estimates for fully-discrete state, adjoint and control and discuss the choice of the stabilization parameter by applying backward Euler method in time. We show that by balancing the error terms in the convection dominated regime, optimal convergence rates can be obtained. The numerical results confirm the theoretically observed convergence rates.
TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS

Suggestions

Variational time discretization methods for optimal control problems governed by diffusion-convection-reaction equations
Akman, Tugba; Karasözen, Bülent (2014-12-15)
In this paper, the distributed optimal control problem governed by unsteady diffusion-convection-reaction equation without control constraints is studied. Time discretization is performed by variational discretization using continuous and discontinuous Galerkin methods, while symmetric interior penalty Galerkin with upwinding is used for space discretization. We investigate the commutativity properties of the optimize-then-discretize and discretize-then-optimize approaches for the continuous and discontinuo...
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.
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...
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
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. ...
Citation Formats
T. Akman, B. Karasözen, and Z. Kanar-Seymen, “STREAMLINE UPWIND/PETROV GALERKIN SOLUTION OF OPTIMAL CONTROL PROBLEMS GOVERNED BY TIME DEPENDENT DIFFUSION-CONVECTION-REACTION EQUATIONS,” TWMS JOURNAL OF APPLIED AND ENGINEERING MATHEMATICS, pp. 221–235, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54100.