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 …

Since the nonconforming P1 finite element method for the Stokes equations was introduced
by M. Crouzeix and PA Raviart in 1973, there have been many advances in the finite …

This paper derives a posteriori error estimates for conforming numerical approximations of
the Laplace eigenvalue problem with a homogeneous Dirichlet boundary condition. In …

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

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 …

In this paper, we apply EQ 1 rot nonconforming finite element to approximate Signorini
problem. If the exact solution u ∈ H^ 5 2\left (Ω\right), the error estimate of order O (h) about …

This paper develops a general framework for a posteriori error estimates in numerical
approximations of the Laplace eigenvalue problem, applicable to all standard numerical …

This article is devoted to studying the application of the weak Galerkin (WG) finite element
method to the elliptic eigenvalue problem with an emphasis on obtaining lower bounds. The …

This paper presents a posteriori error estimates for conforming numerical approximations of
eigenvalue clusters of second-order self-adjoint elliptic linear operators with compact …

We propose a simple method to obtain sharp upper bounds for the interpolation error
constants over the given triangular elements. These constants are important for analysis of …