A Numerical Method to Verify the Elliptic Eigenvalue Problems Including a niqueness Property

摘要

We propose a numerical method to enclose the eigenvalues and eigenfunctions of second-order elliqtic 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 eign-values and eigenfunctions.This local uniqueness assures the simplicity of the eigenvalue. Numerical examples are presented.