On the coupling of MIXED-FEM and BEM for an exterior Helmholtz problem in the plane

Abstract

This paper deals with an elliptic boundary value problem posed in the plane, with variable coefficients, but whose restriction to the exterior of a bounded domain Ω reduces to a Helmholtz equation. We consider a mixed variational formulation in a bounded domain Ω that contains the heterogeneous medium, coupled with a boundary integral method applied to the Helmholtz equation in **. We utilize suitable auxiliary problems, duality arguments, and Fredholm alternative to show that the resulting formulation of the problem is well posed. Then, we define a corresponding Galerkin scheme by using rotated Raviart-Thomas subspaces and spectral elements (on the interface). We show that the discrete problem is uniquely solvable and convergent and prove optimal error estimates. Finally we illustrate our analysis with some results from computational experiments.