We study the approximation properties of shallow neural networks with an activation function
which is a power of the rectified linear unit. Specifically, we consider the dependence of the …

A multigrid method is proposed to solve the eigenvalue problem by the finite element
method based on the combination of the multilevel correction scheme for the eigenvalue …

The integral fractional Laplacian of order s∈(0,1) is a nonlocal operator. It is known that
solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary …

In this work, we revisit the marking decisions made in the standard adaptive finite element
method (AFEM). Experience shows that a naïve marking policy leads to inefficient use of …

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 …

In this paper, an adaptive finite element method is proposed for solving Kohn–Sham
equation with the multilevel correction technique. In the method, the Kohn–Sham equation is …

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

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 …

When using finite element and finite difference methods to approximate eigenvalues of 2m
th-order elliptic problems, the number of reliable numerical eigenvalues can be estimated in …

In this paper, we present a nonnested augmented subspace algorithm and its multilevel
correction method for solving elliptic eigenvalue problems with curved interfaces. The …