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

A new finite element approach for the Dirichlet eigenvalue problem