2016

12. December 2016, 11h (CMAP, Ecole polytechnique, Salle de conf.)

On properties of finite element discretized Dirichlet control problems in polygonal domains

Johannes Pfefferer (Technische Universität München)

Abstract: In this talk we discuss convergence results for finite element discretized Dirichlet control
problems in polygonal domains. We investigate unconstrained as well as control constrained problems.
In both cases we discretize the state and the control by piecewise linear and continuous functions.
The error estimates, which we obtain, mainly depend on the size of the interior angles but also on
the presence of control constraints and the structure of the underlying mesh. For instance,
considering non-convex domains, the convergence rates of the discrete optimal controls in the unconstrained
case can even be worse than in the control constrained case.