Adaptive discontinuous Galerkin (DG) methods for state constrained optimal control problems governed by convection dominated equations

2013-07-19
Yücel, Hamdullah
Benner, Peter
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 the structure of the convection. Discontinuous Galerkin methods became recently as an alternative to the finite difference and finite volume methods for solving wave dominated problems like convection diffusion equation since they possess higher accuracy and work better in complex geometries. In this talk, we will generally focus on analysis and application of discontinuous Galerkin (DG) methods for distributed optimal control problems governed by convection dominated PDEs with state constraints. State constraints are regularized by Lavrentiev-based (mixed control-state constraint) and MoreauYosida-based techniques. We provide an efficient and reliable estimates for the discretization errors in the state, a regularized adjoint and the control. To solve the problem numerically, a primal-dual active set strategy is implemented. Numerical examples are given to illustrate the performance of the error estimator
3rd European Conference on Computational Optimization 2013 (17 - 19 Temmuz 2013)

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Citation Formats
H. Yücel and P. Benner, “Adaptive discontinuous Galerkin (DG) methods for state constrained optimal control problems governed by convection dominated equations,” presented at the 3rd European Conference on Computational Optimization 2013 (17 - 19 Temmuz 2013), Chemnitz, Germany, 2013, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/72482.