A Posteriori Error Estimator for Spectral Approximations of Completely Continuous Operators

Abstract

In this paper, we study numerical approximations of eigenvalues when using projection method for spectral approximations of completely continuous operators. We improve the theory depending on the ascent of $T - \mu$ and provide a new approach for error estimate, which depends only on the ascent of $T_h - \mu_h$. Applying this estimator to the integral operator eigenvalue problems, we obtain asymptotically exact indicators. Numerical experiments are provided to support our theoretical conclusions.