# Adaptive Finite Element Method for Dirichlet Control-Constrained Optimal Control

Fernando Gaspoz*

The aim of this talk is to present, discuss and analyze the a posteriori estimation and convergence for an adaptive finite element method for optimal control problem with constrained Dirichlet control of the form $$\min_{u\in\mathbb{U}_{\text{ad}}} \frac12 \|y-y_d\|_{L^2(\Omega)}^2 + \frac{\alpha}2 \|u\|_{H^{\frac12}(\partial\Omega)}^2 \notag$$ subject to \begin{aligned} -\Delta y &= f \qquad \text{in } \Omega \\ y&=u \qquad \text{on } \partial\Omega, \end{aligned}\notag and $\mathbb{U}_{\text{ad}} =\{ u \in H^{\frac12}(\partial\Omega) : a\leq u\leq b\}$.

Mathematics Subject Classification: 49M25 65N30

Keywords: Optimal Control; Adaptive Finite Element Method

Minisymposion: Adaptivity and Model Order Reduction in PDE Constrained Optimization