  We study a posteriori error analysis of linear-quadratic boundary control
problems under bilateral box constraints on the control which acts through a
Neumann type boundary condition. We adopt the hybridizable discontinuous
Galerkin method as discretization technique, and the flux variables, the scalar
variables and the boundary trace variables are all approximated by polynomials
of degree k. As for the control variable, it is discretized by the variational
discretization concept. Then an efficient and reliable a posteriori error
estimator is introduced, and we prove that the error estimator provides an
upper bound and a lower bound for the error. Finally, numerical results are
presented to illustrate the performance of the obtained a posteriori error
estimator.
