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 …

Assume that $ V_h $ is a space of piecewise polynomials of a degree less than $ r\geq 1$
on a family of quasi-uniform triangulation of size $ h $. There exists the well-known upper …

The paper deals with error estimates and lower bound approximations of the Steklov
eigenvalue problems on convex or concave domains by nonconforming finite element …

We present a general numerical method for computing guaranteed two-sided bounds for
principal eigenvalues of symmetric linear elliptic differential operators. The approach is …

In this paper, we discuss the a posteriori error estimates and adaptive algorithm of non-
conforming mixed finite elements including the Crouzeix–Raviart element and the enriched …

An algorithm is proposed to give explicit lower bounds of the Stokes eigenvalues by utilizing
two nonconforming finite element methods: Crouzeix–Raviart (CR) element and enriched …

In this paper, a multilevel correction scheme is proposed to solve the Steklov eigenvalue
problem by nonconforming finite element methods. With this new scheme, the accuracy of …

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 …

We compare three finite element‐based methods designed for two‐sided bounds of
eigenvalues of symmetric elliptic second order operators. The first method is known as the …

In this paper, a type of multi-level correction scheme is proposed to solve eigenvalue
problems by nonconforming finite element methods. With this new scheme, the accuracy of …