  We begin an investigation of hybridizable discontinuous Galerkin (HDG)
methods for approximating the solution of Dirichlet boundary control problems
governed by elliptic PDEs. These problems can involve atypical variational
formulations, and often have solutions with low regularity on polyhedral
domains. These issues can provide challenges for numerical methods and the
associated numerical analysis. We propose an HDG method for a Dirichlet
boundary control problem for the Poisson equation, and obtain optimal a priori
error estimates for the control. Specifically, under certain assumptions, for a
2D convex polygonal domain we show the control converges at a superlinear rate.
We present 2D and 3D numerical experiments to demonstrate our theoretical
results.
