We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex eigenvalues and eigenfunctions. With the aid of the compact operators theory, we prove that for inf-sup stable finite elements the convergence holds and hence, error estimates for the eigenvalues and eigenfunctions are derived. We also propose an a posteriori error estimator which results to be reliable and efficient. We report a series of numerical tests in two and three dimension in order to assess the performance of the method and the proposed estimator.

翻译：本文提出并分析了一种用于求解Oseen特征值问题的有限元方法。该问题是Stokes特征值问题的推广，其中对流项的存在导致问题变为非对称，进而产生复特征值和复特征函数。借助紧算子理论，我们证明了对于满足inf-sup条件的稳定有限元，收敛性成立，并由此推导出特征值和特征函数的误差估计。我们还提出了一种后验误差估计子，该估计子具有可靠性和高效性。为评估所提方法及估计子的性能，我们报告了一系列二维和三维数值实验。