  In this paper, we propose a new finite element approach, which is different
than the classic Babuska-Osborn theory, to approximate Dirichlet eigenvalues.
The Dirichlet eigenvalue problem is formulated as the eigenvalue problem of a
holomorphic Fredholm operator function of index zero. Using conforming finite
elements, the convergence is proved using the abstract approximation theory for
holomorphic operator functions. The spectral indicator method is employed to
compute the eigenvalues. A numerical example is presented to validate the
theory.
