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.

翻译：本文对arXiv:2004.03523中提出的协调离散化方法以及arXiv:2105.073中提出的非连续伽辽金体积离散化方法，针对时谐亥姆霍兹问题的有限元-边界元耦合方法进行了波数显式分析。我们证明，当$kh/p$充分小且$\log(k)/p$有界时，协调方法与非连续伽辽金方法均具有拟最优性，其中$k$为波数，$h$为网格尺寸，$p$为近似阶数。该分析基于三场耦合公式的$k$显式正则性理论。