Int. J. Numer. Anal. Mod., 5 (2008), pp. 570-589.


A local computational scheme for higher order finite element value approximation

X. Dai 1, L. Shen 2, A. Zhou 3

1 LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing 100080, China and, Graduate University of Chinese Academy of Sciences, Beijing 100080, China
2 Department of Mathematics, Capital Normal University, Beijing 100037, China
3 LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O. Box 2719, Beijing

Received by the editors June 9, 2007 and, in revised form, October 10, 2007.
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.

AMS subject classifications: 65N15, 65N25, 65N30, 65N50.
Key words: eigenvalue; finite element; higher order; local computation
 

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