Nitsche's method for elliptic Dirichlet boundary control problems on curved domains.

We consider Nitsche's method for solving elliptic Dirichlet boundary control problems on curved domains with control constraints. By using Nitsche's method for the treatment of inhomogeneous Dirichlet boundary conditions, the L² boundary control enters in the variational formulation in a natural sense. The idea was first used in Chang, et al. (Math. Anal. Appl.453, 529–557 2017) where the curved boundary was approximated by a broken line and a locally defined mapping was needed to obtain the numerical control on the curved boundary. In this paper, we develop a method defined on curved domains directly. We derive a priori estimates of quasi-optimal order for the control in the L² norm, and quasi-optimal order for the state and adjoint state in energy norms. Numerical examples are provided to show the performance of the proposed method. [ABSTRACT FROM AUTHOR]