Hamdullah Yücel

Hamdullah Yücel
Middle East Technical University | METU · Institute of Applied Mathematics "IAM"

14.99

About

21
Publications
2,246
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
129
Citations
Research Experience
October 2012 - September 2015
Max Planck Institute for Dynamics of Complex Technical Systems
Position
  • PostDoc Position
September 2007 - September 2012
Middle East Technical University
Position
  • Research Assistant

Publications

Publications (21)
Article
We study goal–oriented a posteriori error estimates for the numerical approximation of Dirichlet boundary control problem governed by a convection diffusion equation with pointwise control constraints on a two dimensional convex polygonal domain. The local discontinuous Galerkin method is used as a discretization technique since the control variabl...
Preprint
Full-text available
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a sytem of deterministic convection diffusion equations, is used to handle the stochastic domain in this study, whereas disconti...
Article
Full-text available
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 funct...
Presentation
Partial differential equations (PDEs) with random input data is one of the most powerful tools to model oil and gas production as well as groundwater pollution control. However, the information available on the input data is very limited, which cause high level of uncertainty in approximating the solution to these problems. To identify the random c...
Article
Fractional differential equations are becoming increasingly popular as a modelling tool todescribe a wide range of non-classical phenomena with spatial heterogeneities throughout the appliedsciences and engineering. However, the non-local nature of the fractional operators causes essentialdifficulties and challenges for numerical approximations. We...
Article
Full-text available
In this paper, we investigate numerical solution of Allen–Cahn equation with constant and degenerate mobility, and with polynomial and logarithmic energy functionals. We discretize the model equation by symmetric interior penalty Galerkin (SIPG) method in space, and by average vector field (AVF) method in time. We show that the energy stable AVF me...
Article
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 funct...
Technical Report
Full-text available
In this paper, we consider Dirichlet boundary control of a convection-diffusion equation with L 2 – 4 boundary controls subject to pointwise bounds on the control posed on a two dimensional convex polygonal domain. 5 We use the local discontinuous Galerkin method as a discretization method. We derive a priori error estimates for 6 the approximation...
Article
Full-text available
We investigate smooth and sparse optimal control problems for convective FitzHugh-Nagumo equation with travelling wave solutions in moving excitable media. The cost function includes distributed space-time and terminal observations or targets. The state and adjoint equations are discretized in space by symmetric interior point Galerkin (SIPG) metho...
Article
Full-text available
We investigate an a posteriori error analysis of adaptive finite element approximations of linearquadratic boundary optimal control problems under bilateral box constraints, which act on a Neumann boundary control. We use a symmetric interior penalty Galerkin (SIPG) method as discretization technique. An efficient and reliable residual-type error e...
Article
Full-text available
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 es...
Chapter
Full-text available
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...
Article
Full-text available
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...
Article
We apply two different strategies for solving unsteady distributed optimal control problems governed by diffusion–convection–reaction equations. In the first approach, the optimality system is transformed into a biharmonic equation in the space–time domain. The system is then discretized in space and time simultaneously and solved by an equation-ba...
Article
Full-text available
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, whic...
Article
Full-text available
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 me...
Article
Full-text available
In this paper, convection-diffusion-reaction models with nonlinear reaction mechanisms, which are typical problems of chemical systems, are studied by using the upwind symmetric interior penalty Galerkin (SIPG) method. The local spurious oscillations are minimized by adding an artificial viscosity diffusion term to the original equations. A discont...
Conference Paper
Full-text available
We discuss the numerical solution of linear quadratic optimal control problem with distributed and Robin boundary controls governed by diffusion convection reaction equations. The discretization is based on the upwind symmetric interior penalty Galerkin (SIPG) methods which lead to the same discrete scheme for the “optimize-then-discretize” and the...
Conference Paper
Full-text available
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...
Article
Full-text available
We prove residual based a-posteriori error estimates for the solution of distributed linear-quadratic optimal control problems governed by an elliptic convection dif-fusion partial differential equation (PDE) using the symmetric interior penalty discontinuous Galerkin (SIPG) method with upwinding for the convection term, and we demonstrate the appl...

Network

Cited By

Projects