FEM-BEM coupling for the high-frequency Helmholtz problem

We present a wavenumber-explicit analysis of FEM-BEM coupling methods for time-harmonic Helmholtz problems proposed in arXiv:2004.03523 for conforming discretizations and in arXiv:2105.06173 for discontinuous Galerkin (DG) volume discretizations. We show that the conditions that $kh/p$ be sufficiently small and that log(k) / p be bounded imply quasi-optimality of both conforming and DG-method, where k is the wavenumber, h the mesh size, and p the approximation order. The analysis relies on a k-explicit regularity theory for a three-field coupling formulation.