Goal–oriented a posteriori error estimation for Dirichlet boundary control problems

Download

10.1016:j.cam.2020.113012.pdf

Date

2021-1

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

407
views

278
downloads

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 the complementary system due to the discretization. Numerical examplesare presented to illustrate the performance of the proposed estimator.

Subject Keywords

Applied Mathematics, Computational Mathematics, Dirichlet boundary optimal control, Local discontinuous Galerkin, Goal–oriented adaptivity, A posteriori error estimate, Convection diffusion equation

URI

https://hdl.handle.net/11511/50722

Journal

Journal of Computational and Applied Mathematics

DOI

https://doi.org/10.1016/j.cam.2020.113012

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

A local discontinuous Galerkin method for Dirichlet boundary control problems Yücel, Hamdullah (null; 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.
Adaptive discontinuous Galerkin methods for state constrained optimal control problems governed by convection diffusion equations Yücel, Hamdullah (2015-09-01) 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 derive different residual-based error indicators for each regularization technique due to the regularity issues. An adaptive mesh refinement indicated by a poste...
Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equations Stoll, Martin; Yücel, Hamdullah; Benner, Peter (2018-01-01) 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 functional. Residual-based error estimators are proposed for both approaches. The derived error estimators are used as error indicators to guide the mesh refinements. ...
Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints Yücel, Hamdullah; Karasözen, Bülent (2014-01-02) 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 mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented for convection dominated problems to illustrate the theoretic...
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.

Citation Formats

H. Yücel, “Goal–oriented a posteriori error estimation for Dirichlet boundary control problems,” Journal of Computational and Applied Mathematics, 2021, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/50722.