FEM-BEM coupling for the high-frequency Helmholtz problem

Abstract

Abstract We present a wavenumber-explicit analysis of the FEM-BEM coupling methods for time-harmonic Helmholtz problems proposed in [1] for conforming discretizations and in [2] for discontinuous Galerkin (DG) volume discretizations. We show that the conditions that kh / p be sufficiently small and that $$\log (k) / p$$ 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.