In this paper we analyze a nonconforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. The spaces under consideration lead to a divergence-free method which is capable to capture properly the divergence at discrete level and the eigenvalues and eigenfunctions. Under the compact theory for operators we prove convergence and error estimates for the method. By employing the theory of compact operators we recover the double order of convergence of the spectrum. Finally, we present numerical tests to assess the performance of the proposed numerical scheme.

翻译：本文分析了一种用于逼近二维 Oseen 特征值问题的特征函数与特征值的非协调虚拟元方法。所考虑的空间导出一个散度自由方法，该方法能够在离散层面恰当地捕捉散度、特征值及特征函数。基于算子的紧性理论，我们证明了该方法的收敛性并给出了误差估计。通过运用紧算子理论，我们恢复了谱的二阶收敛性。最后，我们通过数值实验评估了所提数值格式的性能。