The Validity of Johnson-Nedelec's BEM-FEM Coupling on Polygonal Interfaces

In this short article we prove that the classical one-equation (or Johnson-Nedelec) oupling of finite and boundary elements can be applied with a Lipschitz coupling interface. Because of the way it was originally approached from the analytical standpoint, this BEM-FEM scheme has generally required smooth boundaries and hence produced a consistency error in the finite element part. With a variational argument, we prove that this requirement is not needed and that stability holds for all pairs of discrete space, as it inherits the underlying ellipticity of the problem.