Residual based a posteriori error estimation for Dirichlet boundary control problems

Date

2021-09-01

Author

Yücel, Hamdullah

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

242
views

0
downloads

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 naturally exists in the variational form due to its mixed finite element structure. We also demonstrate the application of our a posteriori error estimator for the adaptive solution of these optimal control problems.

URI

https://hdl.handle.net/11511/92332

DOI

https://doi.org/10.1051/proc/202171185

Conference Name

FGS’2019 - 19th French-German-Swiss conference on Optimization

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

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 ...
Boundary element method solution of initial and boundary value problems in fluid dynamics and magnetohydrodynamics Bozkaya, Canan; Tezer, Münevver; Department of Mathematics (2008) In this thesis, the two-dimensional initial and boundary value problems invol\-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems Bozkaya, Canan (2005-03-18) The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Exponential Smoothing of Multiple Reference Frame Components With GPUs for Real-Time Detection of Time-Varying Harmonics and Interharmonics of EAF Currents Balouji, Ebrahim; Salor, Ozgul; Ermiş, Muammer (2018-11-01) In this research work, a multiple synchronous reference frame (MSRF)-based analysis method, used together with exponential smoothing (ES) to accurately obtain the time-varying harmonics and interharmonics of electric arc furnace (EAF) currents, is proposed. The proposed method has been implemented on NVIDIA Geforce GTX 960 graphics card for the parallel processing of all harmonics and interharmonics so that real-time processing of the EAF currents obtained from a measurement point of the electricity transmi...
Exponential smoothing of multiple reference frame components with GPUs for real-time detection of time-varying harmonics and interharmonics of EAF currents Balouji, Ebrahim; SALOR DURNA, ÖZGÜL; Ermiş, Muammer (2017-10-01) In this research work, a multiple synchronous reference frame (MSRF) based analysis method used together with exponential smoothing (ES) to accurately obtain the time-varying harmonics and interharmonics of electric arc furnace (EAF) currents, is proposed. The proposed method has been implemented on NVIDIA Geforce GTX 960 graphics card for the parallel processing of all harmonics and interharmonics so that real-time processing of the EAF currents obtained from a measurement point of the electricity transmis...

Citation Formats

H. Yücel, “Residual based a posteriori error estimation for Dirichlet boundary control problems,” Nice, Fransa, 2021, vol. 71, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/92332.