Optimal Control of Diffusion Convection Reaction Equations Using Upwind Symmetric Interior Penalty Galerkin SIPG Method

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 discretize-then-optimize.


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.
Analysis of a projection-based variational multiscale method for a linearly extrapolated BDF2 time discretization of the Navier-Stokes equations
Vargün, Duygu; Kaya Merdan, Songül; Department of Mathematics (2018)
This thesis studies a projection-based variational multiscale (VMS) method based on a linearly extrapolated second order backward difference formula (BDF2) to simulate the incompressible time-dependent Navier-Stokes equations (NSE). The method concerns adding stabilization based on projection acting only on the small scales. To give a basic notion of the projection-based VMS method, a three-scale VMS method is explained. Also, the principles of the projection-based VMS stabilization are provided. By using t...
Least-squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of diffusive-convective problems
Bozkaya, Canan (Elsevier BV, 2007-01-01)
Least-squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in diffusive-convective type problems with variable coefficients. The DRBEM enables us to use the fundamental solution of Laplace equation, which is easy to implement computation ally. The terms except the Laplacian are considered as the nonhomogeneity in the equation, which ar...
Numerical solution of nonlinear reaction-diffusion and wave equations
Meral, Gülnihal; Tezer, Münevver; Department of Mathematics (2009)
In this thesis, the two-dimensional initial and boundary value problems (IBVPs) and the one-dimensional Cauchy problems defined by the nonlinear reaction- diffusion and wave equations are numerically solved. The dual reciprocity boundary element method (DRBEM) is used to discretize the IBVPs defined by single and system of nonlinear reaction-diffusion equations and nonlinear wave equation, spatially. The advantage of DRBEM for the exterior regions is made use of for the latter problem. The differential quad...
Nonautonomous Bifurcations in Nonlinear Impulsive Systems
Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01)
In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.
Citation Formats
B. Karasözen and H. Yücel, “Optimal Control of Diffusion Convection Reaction Equations Using Upwind Symmetric Interior Penalty Galerkin SIPG Method,” 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32133.