@techreport{Jehle2018PODba-42857,
  year={2018},
  series={Konstanzer Schriften in Mathematik},
  title={POD-based augmented Lagrangian method for state constrained heat-convection phenomena},
  number={377},
  author={Jehle, Jonas Siegfried and Mechelli, Luca and Volkwein, Stefan},
  note={Konferenz: IUTAM Symposium 2018, 22. Mai 2018 - 25. Mai 2018, Stuttgart}
}

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    <dcterms:abstract xml:lang="eng">We consider an optimal boundary control problem of the heat equation with convection with bilateral control and state constraints. The goal is to keep the temperature (state) within a desired range while the norm of the boundary controls is minimized. To numerically approximate the unique solution of the problem, a first-order augmented Lagrangian method is utilized. The gradient of the augmented Lagrangian is characterized by the solution of the adjoint equation. To decrease the computational time, we apply a reduced-order approach based on proper orthogonal decomposition (POD). To gain a sufficiently accurate approximation, we propose and compare different manners to compute the snapshots and thus the POD basis. Numerical tests compare the efficiency of the proposed strategies.</dcterms:abstract>
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