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 numerical upscaling techniques for a class of linear second-order self-adjoint
elliptic partial differential operators (or their high-resolution finite element discretization). As …

Abstract The Adaptive Finite Element Method (AFEM) for approximating solutions of PDE
boundary value and eigenvalue problems is a numerical scheme that automatically and …

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 paper presents a combined adaptive finite element method with an iterative algebraic
eigenvalue solver for a symmetric eigenvalue problem of asymptotic quasi-optimal …

In this paper, we study an adaptive finite element for multiple eigenvalues of second order
elliptic partial differential equations. We obtain both the asymptotic contraction property and …

We address the problem of rigorously bounding the errors in the numerical solution of the
Kohn–Sham equations due to (i) the finiteness of the basis set,(ii) the convergence …

This paper proposes and analyzes an a posteriori error estimator for the finite element multi-
scale discretization approximation of the Steklov eigenvalue problem. Based on the a …

This paper presents adaptive algorithms for eigenvalue problems associated with non-
selfadjoint partial differential operators. The basis for the developed algorithms is a …

Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and
numerically tested. The methods combine advantages of the two-grid algorithm (Xu and …