Hamdullah Yücel

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

We investigate a numerical behavior of robust deterministic optimal control problem subject to a convection-diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing uncertainties into a large system of deterministic problems, is applied to discretize the stochastic domain, wh...

In this paper, we focus on a numerical investigation of a strongly convex and smooth optimization problem subject to a convection–diffusion equation with uncertain terms. Our approach is based on stochastic approximation where true gradient is replaced by a stochastic ones with suitable momentum term to minimize the objective functional containing...

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 system of deterministic convection diffusion equations, is used to handle the stochastic domain in this study, whereas discont...

We investigate a numerical behaviour of robust deterministic optimal control problem governed by a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach , turning the original stochastic problem into a system of deterministic problems, is used to handle the stochast...

We study a residual–based a posteriori error estimate for the solution of Dirichlet boundary control problem governed by a convection diffusion equation on a two dimensional convex polygonal domain, using the local discontinuous Galerkin (LDG) method with upwinding for the convection term. With the usage of LDG method, the control variable naturall...

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 system of deterministic convection diffusion equations, is used to handle the stochastic domain in this study, whereas discont...

While control and user (data) plane separation (CUPS) through clustering improves the scalability of ad hoc networks in comparison to flat topologies, it introduces additional challenges for resource scheduling when contention-free medium access is employed. This paper addresses intra- and inter-cluster link scheduling problem in multi-channel ad h...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...