A local discontinuous Galerkin method for Dirichlet boundary control problems

2018-10-20
In this paper, we consider Dirichlet boundary control of a convection-diffusion equation with L 2 4 – 5 boundary controls subject to pointwise bounds on the control posed on a two dimensional convex polygonal domain. 6 We use the local discontinuous Galerkin method as a discretization method. We derive a priori error estimates for 7 the approximation of the Dirichlet boundary control problem on a polygonal domain. Several numerical results are 8 provided to illustrate the theoretical results.
BEYOND: Workshop on Computational Science and Engineering (20 - 21 Ekim 2018)

Suggestions

Goal–oriented a posteriori error estimation for Dirichlet boundary control problems
Yücel, Hamdullah (Elsevier BV, 2021-1)
We study goal-oriented a posteriori error estimates for the numerical approximation ofDirichlet boundary control problem governed by a convection diffusion equation withpointwise control constraints on a two dimensional convex polygonal domain. The localdiscontinuous Galerkin method is used as a discretization technique since the controlvariable is involved in a variational form in a natural sense. We derive primal–dualweightederrorestimatesfortheobjectivefunctionalwithanerrortermrepresentingthemismatch in ...
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.
A discontinuous Galerkin method for optimal control problems governed by a system of convection-diffusion PDEs with nonlinear reaction terms
Yücel, Hamdullah; BENNER, Peter (2015-11-01)
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 estimator for the state and the adjoint variables. An adaptive mesh refinement indicated by a posteriori error estimates is applied. The arising saddle point system...
A Non-Galerkin Spatial-Domain Approach for Efficient Calculation of the Dispersion Characteristics of Microstrip Lines
Guedue, Tamer; Alatan, Lale (2008-07-11)
In the analysis of dispersion characteristics of microstrip lines, spectral domain approaches has been preferred as opposed to the spatial domain calculations since the spatial domain Green's functions corresponding to the microstrip structure require the numerical evaluation of inverse Fourier transform integrals which are computationally expensive. However as demonstrated in Bernal, J. et al, (2000), the discrete complex image representation of the spatial domain Greenpsilas functions eliminates the need ...
An integral equation approach to the computation of nonlinear fields in electrical machines
Kükrer, Osman; Ertan, H. Bülnet (Institute of Electrical and Electronics Engineers (IEEE), 1988-7)
A numerical method based on an integral equation formulation, for the computation of nonlinear magnetostatic field, in two dimensions in cylindrical polar coordinates is given. The correctness of the method is illustrated by solving two linear two-dimensional magnetic field problems which have readily available analytical solutions. The dependence of the accuracy of the solution on the number and distribution of the meshes is studied on these examples. The method is then applied to the computation of the no...
Citation Formats
H. Yücel, “A local discontinuous Galerkin method for Dirichlet boundary control problems,” presented at the BEYOND: Workshop on Computational Science and Engineering (20 - 21 Ekim 2018), Ankara, Türkiye, 2018, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/78646.