Abstract.
We propose a numerical method to enclose the eigenvalues and eigenfunctions of second-order elliptic operators with local uniqueness. We numerically construct a set containing eigenpairs which satisfies the hypothesis of Banach's fixed point theorem in a certain Sobolev space by using a finite element approximation and constructive error estimates. We then prove the local uniqueness separately of eigenvalues and eigenfunctions. This local uniqueness assures the simplicity of the eigenvalue. Numerical examples are presented.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: November 2, 1998; revised June 5, 1999
Rights and permissions
About this article
Cite this article
Nagatou, K. A Numerical Method to Verify the Elliptic Eigenvalue Problems Including a Uniqueness Property. Computing 63, 109–130 (1999). https://doi.org/10.1007/s006070050054
Issue Date:
DOI: https://doi.org/10.1007/s006070050054