A Local Computational Scheme for Higher Order Finite Element Eigenvalue Approximations

Abstract

Based on some coupled discretizations, a local computational scheme is proposed and analyzed in this paper for a class of higher order finite element eigenvalue approximations. Its efficiency is proven by theoretical and numerical evidences. It is shown that the solution of an eigenvalue problem in a higher order finite element space may be reduced to the solution of an eigenvalue problem in a lower order finite element space, and the solutions of some linear algebraic systems in the higher order finite element space by some local and parallel procedure.