A virtual element method for the acoustic vibration problem

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.

References in corpus (6)

• On the Virtual Element Method for Three-Dimensional Elasticity Problems on Arbitrary Polyhedral Meshes
• A Hybrid High-Order method for the incompressible Navier--Stokes equations based on Temam's device
• A Virtual Element Method for elastic and inelastic problems on polytope meshes
• Mixed Virtual Element Methods for general second order elliptic problems on polygonal meshes
• The nonconforming virtual element method
• Multigrid algorithms for $hp$-version Interior Penalty Discontinuous Galerkin methods on polygonal and polyhedral meshes

Cited by in corpus (3)

• Lowest order Virtual Element approximation of magnetostatic problems
• A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem
• A posteriori error estimates for a Virtual Elements Method for the Steklov eigenvalue problem