FEM-BEM coupling for the high-frequency Helmholtz problem
<|reference_start|>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.<|reference_end|>
@article{melenk2024fem-bem,
    title={FEM-BEM coupling for the high-frequency Helmholtz problem},
    author={Jens Markus Melenk, Ilaria Perugia, Alexander Rieder},
    journal={arXiv preprint arXiv:2407.04428},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.04428},
    primaryClass={math.NA cs.NA}
}