Enhancing eigenvalue approximation with Bank--Weiser error estimators

Abstract

In this paper we propose a way of enhancing eigenvalue approximations with the Bank--Weiser error estimators for the $P1$ and $P2$ conforming finite element methods of the Laplace eigenvalue problem. It is shown that we can achieve two extra orders of convergence than those of the original eigenvalue approximations when the corresponding eigenfunctions are smooth and the underlying triangulations are strongly regular. Some numerical results are presented to demonstrate the accuracy of the enhanced eigenvalue approximations.