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

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2018-01-01

Author

Stoll, Martin
Yücel, Hamdullah
Benner, Peter

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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. A symmetric interior penalty Galerkin method in space and a backward Euler method in time are applied in order to discretize the optimization problem. Numerical results are presented, which illustrate the performance of the proposed error estimators.

Subject Keywords

Optimal control problem, A posteriori error estimate, Discontinuous Galerkin method, Convection diffusion equations

URI

https://hdl.handle.net/11511/32323

Journal

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS

DOI

https://doi.org/10.1553/etna_vol48s407

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

M. Stoll, H. Yücel, and P. Benner, “Adaptive discontinuous Galerkin approximation of optimal control problems governed by transient convection-diffusion equations,” ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, pp. 407–434, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32323.