For eigenvalue problems of self-adjoint differential operators, a universal framework is
proposed to give explicit lower and upper bounds for the eigenvalues. In the case of the …

To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem,
an enhanced version of the eigenvalue estimation algorithm developed by the third author is …

The finite element method (FEM) is applied to bound leading eigenvalues of the Laplace
operator over polygonal domains. Compared with classical numerical methods, most of …

This note studies the first non-trivial eigenvalue of second order self-adjoint elliptic operators
in Rd. Some lower bounds of the eigenvalue are obtained by using a probabilistic approach …

In this paper, we propose a numerical method to verify bounds for multiple eigenvalues for
elliptic eigenvalue problems. We calculate error bounds for approximations of multiple …

We introduce some ways to compute the lower and upper bounds of the Laplace eigenvalue
problem. By using the special nonconforming finite elements, ie, enriched Crouzeix-Raviart …

This is a survey article about using non-conforming finite elements in solving eigenvalue
problems of elliptic operators, with emphasis on obtaining lower bounds. In addition, this …

New approaches for computing tight lower bounds to the eigenvalues of a class of
semibounded self-adjoint operators are presented that require comparatively little a priori …

This paper is a complement of the work (Hu et al. in arXiv: 1112.1145 v1 math. NA, 2011),
where a general theory is proposed to analyze the lower bound property of discrete …

1. Introduction. This paper gives lower bounds for all the eigenvalues of an arbitrary second
order self-adjoint elliptic differential operator on a bounded domain R with zero boundary …