The Postprocess Of Eigenvalue Problem

Post-processing problem of Eigenvalue is to make the recovery eigenvalue has superconvergence with some post-processing tech-nology applied in solutions of finite element method and it’s deriva-tive values.For the finite element method,derivatives always don’t have superconvergence at the nodes;so it’s is very important to construct a good derivative recovery operator.Currently,there are some popular method in the construction of derivative recovery op-erator,like SPR method and PPR method.The PPR method intro-duced by Naga-Zhang in2005,which is used to construct derivative recovery operator.The PPR technique is one of the derivative recovery techniques based on function value,it’s easy to operate and more feasible than others,and can be used in many meshes.This paper want to discuss the superconvergence of recovery eigenvalue based on the existing results.The first chapter of this paper is some basic knowledge,and two eigenvalue recovery technologies are introduced in the second chap-ter,they are eigenvalue recovery technologies base on interpolation techniques and PPR technology.In the second chapter,we can see the good superconvergence results can be achieved with PPR tech-nology applied to post-processing problem of eigenvalue in triangu-lar meshes and rectangular meshes. In some good meshes,recovery eigenvalue of triangular linear problem have superconvergence at a rate of close4,8of rectangular bi-quadratic problem.After careful analysis of the PPR technology,apply the PPR technology with finite element to some simple eigenvalue prob-lem,the recovery eigenvalue can of hybrid grid linear problem can gain good results.