  In their article "Coupling at a distance HDG and BEM", Cockburn, Sayas and
Solano proposed an iterative coupling of the hybridizable discontinuous
Galerkin method (HDG) and the boundary element method (BEM) to solve an
exterior Dirichlet problem. The novelty of the numerical scheme consisted of
using a computational domain for the HDG discretization whose boundary did not
coincide with the coupling interface. In their article, the authors provided
extensive numerical evidence for convergence, but the proof of convergence and
the error analysis remained elusive at that time. In this article we fill the
gap by proving the convergence of a relaxation of the algorithm and providing a
priori error estimates for the numerical solution.
