具有高阶余项的特征值有限元解的渐近展开

ASYMPTOTIC EXPANSION WITH HIGHER ORDER REMAINDER FOR THE F.E.APPROXIMATION OF EIGENVALUES

本文研究多角形域上特征值问题的有限元逼近，利用四边形等参数双线性元，证明了．当特征函值为四边形域时，λｈ＝λ＋ｃ１ｈ２＋ｃ２ｈ４＋Ｏ（ｎ）６．当特征函数，Ω为一般多角形域时，λｈ＝λ＋ｃ１ｈ２＋ｃ２ｈ４＋Ｏ（ｈ５｜ｌｎｈ｜）．

In this paper,we study the eigenvalus problems approximated by finite element method on a convex polygonal domain.We use a kind of blockwise quadrangle partition and isoparemotric bilinear elements,and show that:λh=λ+c1h2+c2h4 + o(h6)if Ω is a quadrangle and the eigenfunction u ∈ H6, and λh=λ+c1h2+c2h4+o(h5|lnh|)if Ω is a general polygonal domain and the eigenfunctin u ∈ H5 ∩ W5,1.