A virtual element method for the acoustic vibration problem

2016/01/17 by L. Beirão da Veiga, da Veiga, Lourenço Beirão, David Mora +5 · 1 citation
Computer Science · Engineering · #65N25 #65N30 #70J30 #76M25 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1601.04316

openalex publication_date 2016/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes

Cited by

• A locking-free mixed virtual element discretization for the two dimensional elasticity eigenvalue problem

Related

• On the stabilization of a virtual element method for an acoustic vibration problem
• Error analysis for a non-conforming virtual element discretization of the acoustic problem
• A posteriori virtual element method for the acoustic vibration problem
• VEM allowing small edges for the acoustic problem
• A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations