# Preconditioning of Optimal Dirichlet Boundary Control Problems in Energy Spaces

Lorenz John* and Olaf Steinbach

We construct and analyze a preconditioner for the discrete optimality system when considering finite element methods for optimal Dirichlet boundary control problems in appropriate energy spaces. In particular, we focus on the robustness with respect to the mesh size and the cost coefficient. The focus is further laid on the case of cost coefficients in $(0,1)$. We present numerical examples illustrating the obtained theoretical results.

Mathematics Subject Classification: 65N30

Keywords: Dirichlet boundary control; energy space; preconditioner; multilevel method

Minisymposion: Preconditioning for PDE-Constrained Optimization