  We show how a Trefftz Discontinuous Galerkin (TDG) method for the
displacement form of the Helmholtz equation can be used to approximate problems
having a generalized impedance boundary condition (GIBC) involving surface
derivatives of the solution. Such boundary conditions arise naturally when
modeling scattering from a scatterer with a thin coating. The thin coating can
then be approximated by a GIBC. A second place GIBCs arise is as higher order
absorbing boundary conditions. This paper also covers both cases. Because the
TDG scheme has discontinuous elements, we propose to couple it to a surface
discretization of the GIBC using continuous finite elements. We prove
convergence of the resulting scheme and demonstrate it with two numerical
examples.
