In this paper, we consider a numerical technique to verify the exact eigenvalues and eigenfunctions of second-order elliptic operators in some neighborhood of their approximations. This technique is based on Nakao's method  using the Newton-like operator and the error estimates for the C0 finite element solution. We construct, in computer, a set containing solutions which satisfies the hypothesis of Schauder's fixed point theorem for compact map on a certain Sobolev space. Moreover, we propose a method to verify the eigenvalue which has the smallest absolute value. A numerical example is presented.
|ジャーナル||Japan Journal of Industrial and Applied Mathematics|
|出版ステータス||Published - 1999 10|
ASJC Scopus subject areas
- Applied Mathematics