Adaptive Symmetric Interior Penalty Galerkin Method for Boundary Control Problems

Date

2015-03-11

Author

Yücel, Hamdullah
Benner, Peter

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https://hdl.handle.net/11511/84639

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ADAPTIVE SYMMETRIC INTERIOR PENALTY GALERKIN METHOD FOR BOUNDARY CONTROL PROBLEMS BENNER, Peter; Yücel, Hamdullah (2017-01-01) We investigate an a posteriori error analysis of adaptive finite element approximations of linear-quadratic boundary optimal control problems under bilateral box constraints, which act on a Neumann boundary control. We use a symmetric interior Galerkin method as discretization technique. An efficient and reliable residual-type error estimator is introduced by invoking data oscillations. We then derive local upper and lower a posteriori error estimates for the boundary control problem. Adaptive mesh refineme...
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...
Adaptive discontinuous Galerkin methods for convection dominated optimal control problems Yücel, Hamdullah; Karasözen, Bülent; Department of Scientific Computing (2012) Many real-life applications such as the shape optimization of technological devices, the identification of parameters in environmental processes and flow control problems lead to optimization problems governed by systems of convection di usion partial di erential equations (PDEs). When convection dominates di usion, the solutions of these PDEs typically exhibit layers on small regions where the solution has large gradients. Hence, it requires special numerical techniques, which take into account the structu...
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 Methods for Nonlinear Diffusion Convection Reaction Equations Karasözen, Bülent; Manguoğlu, Murat (2015-06-15)

Citation Formats

H. Yücel and P. Benner, “Adaptive Symmetric Interior Penalty Galerkin Method for Boundary Control Problems,” 2015, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/84639.