A virtual element method for the acoustic vibration problem
Numerical Analysis
2016-01-19 v1
Abstract
We analyze in this paper a virtual element approximation for the acoustic vibration problem. We consider a variational formulation relying only on the fluid displacement and propose a discretization by means of H(div) virtual elements with vanishing rotor. Under standard assumptions on the meshes, we show that the resulting scheme provides a correct approximation of the spectrum and prove optimal order error estimates. With this end, we prove approximation properties of the proposed virtual elements. We also report some numerical tests supporting our theoretical results.
Cite
@article{arxiv.1601.04316,
title = {A virtual element method for the acoustic vibration problem},
author = {Lourenço Beirão da Veiga and David Mora and Gonzalo Rivera and Rodolfo Rodríguez},
journal= {arXiv preprint arXiv:1601.04316},
year = {2016}
}