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We introduce non conforming virtual elements to approximate the eigenvaluesand eigenfunctions of the two dimensional acoustic vibration problem. We focusour attention on the pressure formulation of the acoustic vibration problem inorder to discretize it with a suitable non conforming virtual space for$\mathrm{H}^1$. With the aid of the theory of non-compact operators we proveconvergence and spectral correctness of the method. To illustrate thetheoretical results, we report numerical tests on different polygonal meshes,in order to show the accuracy of the method on the approximation of thespectrum.

Error analysis for a non-conforming virtual element discretization of the acoustic problem