Multigrid methods for an elliptic optimal control problem with pointwise state constraints

We design multigrid methods for an elliptic distributed optimal control problem with pointwise state constraints. They are based on the P1 finite element method from Brenner et al. (2021), where the optimal control problem was reformulated as a variational inequality for the state variable. The perf...

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Veröffentlicht in:	Results in applied mathematics 2023-02, Vol.17, p.100356, Article 100356
Hauptverfasser:	Brenner, Susanne C., Liu, Sijing, Sung, Li-yeng
Format:	Artikel
Sprache:	eng
Schlagworte:	[formula omitted]1 finite element method Elliptic distributed optimal control problems Multigrid methods P1 finite element method Pointwise state constraints Primal–dual active set algorithm
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Zusammenfassung:	We design multigrid methods for an elliptic distributed optimal control problem with pointwise state constraints. They are based on the P1 finite element method from Brenner et al. (2021), where the optimal control problem was reformulated as a variational inequality for the state variable. The performance of the multigrid methods is illustrated by numerical experiments.
ISSN:	2590-0374 2590-0374
DOI:	10.1016/j.rinam.2023.100356