Title

A new finite element approach for the Dirichlet eigenvalue problem

Document Type

Article

Publication Date

7-2020

Department

Department of Mathematical Sciences

Abstract

We propose a new finite element approach, which is different than the classic Babuška–Osborn theory, to approximate Dirichlet eigenvalues. The problem is formulated as the eigenvalue problem of a holomorphic Fredholm operator function of index zero. The convergence for conforming finite elements 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.

Publication Title

Applied Mathematics Letters

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