  This article examines the Dirichlet boundary control problem governed by the
Poisson equation, where the control variables are square integrable functions
defined on the boundary of a two dimensional bounded, convex, polygonal domain.
It employs an ultra weak formulation and utilizes Crouzeix-Raviart finite
elements to discretize the state variable, while employing piecewise constants
for the control variable discretization. The study demonstrates that the energy
norm of an enriched discrete optimal control is uniformly bounded with respect
to the discretization parameter. Furthermore, it establishes an optimal order a
priori error estimate for the control variable.
