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. Key words. Eigenvalue, finite element, higher order, local computation. 2000 AMS subject classifications. 65N15, 65N25, 65N30, 65N50 1. Introduction. Motivate