This paper proposes and analyzes a BEM-FEM scheme to approximate
a time-harmonic diffusion problem in the plane with non-constant
coefficients in a bounded area. The model is set as a Helmholtz
transmission problem with adsorption and with non-constant
coefficients in a bounded domain. We reformulate the problem as a
four-field system. For the temperature and the heat flux we use
piecewise constant functions and lowest order Raviart-Thomas
elements associated to a triangulation approximating the bounded
domain. For the boundary unknowns we take spaces of periodic
splines. We show how to transmit information from the approximate
boundary to the exact one in an efficient way and prove
well-posedness of the Galerkin method. Error estimates are
provided and experimentally corroborated at the end of the work.