A virtual element method for the acoustic vibration problem
Provides a theoretical foundation for virtual element methods in acoustic vibration, but the contribution is incremental as it extends existing H(div) virtual elements to a new problem.
The authors develop a virtual element method for the acoustic vibration problem, proving optimal error estimates and correct spectral approximation, with numerical tests confirming the theory.
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.