  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.

Numerical Analysis;Numerical Analysis