Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection diffusion equations

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2014-04-11

Author

Yücel, Hamdullah
Benner, Peter

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https://hdl.handle.net/11511/87964

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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 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)
Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations UZUNCA, Murat; Karasözen, Bülent; Manguoğlu, Murat (2014-09-04) In this work, we apply the adaptive discontinuous Galerkin (DGAFEM) method to the convection dominated non-linear, quasi-stationary diffusion convection reaction equations. We propose an efficient preconditioner using a matrix reordering scheme to solve the sparse linear systems iteratively arising from the discretized non-linear equations. Numerical examples demonstrate effectiveness of the DGAFEM to damp the spurious oscillations and resolve well the sharp layers occurring in convection dominated non-line...
Adaptive discontinuous Galerkin (DG) methods for state constrained optimal control problems governed by convection dominated equations Yücel, Hamdullah; Benner, Peter (2013-07-19) 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 diffusion partial differential equations (PDEs). When convection dominates diffusion, the solutions of these PDEs typically exhibit layers, localized regions where the derivative of the solution is large. Hence, it requires special numerical techniques, which take into account...

Citation Formats

H. Yücel and P. Benner, “Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection diffusion equations,” 2014, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/87964.