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.

中文翻译：

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Oseen 特征值问题的有限元分析

我们提出并分析了 Oseen 特征值问题的有限元方法。该问题是斯托克斯特征值问题的扩展，其中对流项的存在导致非对称问题，从而导致复杂的特征值和特征函数。借助紧算子理论，我们证明了对于 inf-sup 稳定有限元，收敛性成立，因此导出了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器，其结果是可靠且高效的。我们报告了一系列二维和三维数值测试，以评估该方法和所提出的估计器的性能。