We introduce non conforming virtual elements to approximate the eigenvalues and eigenfunctions of the two dimensional acoustic vibration problem. We focus our attention on the pressure formulation of the acoustic vibration problem in order 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 prove convergence and spectral correctness of the method. To illustrate the theoretical results, we report numerical tests on different polygonal meshes, in order to show the accuracy of the method on the approximation of the spectrum.

翻译：我们引入非协调虚拟元来逼近二维声学振动问题的特征值与特征函数。我们聚焦于声学振动问题的压力公式，利用适用于$\mathrm{H}^1$空间的非协调虚拟空间对其进行离散。借助非紧算子理论，我们证明了该方法的收敛性与谱正确性。为阐明理论结果，我们报告了在不同多边形网格上的数值实验，展示了该方法在谱逼近中的精度。