Overlapped BEM–FEM for some Helmholtz transmission problems

In this paper we propose and analyse a novel numerical method for a Helmholtz transmission problem in a bounded domain, with non-homogeneous mixed conditions on the exterior boundary. The method relies on the superposition of a classical Lagrange finite element method on a triangulation of the domain without the interior obstacles and a general stable boundary element method for an exterior Helmholtz transmission problem. The analysis of the scheme is carried out by transforming the exact and the approximated equations into an abstract operator equation of the second kind with a non-standard approximation of it. A numerical example for a two dimensional case shows the good behaviour of the method and its advantages for some particular geometries.