在具有光滑曲线边界的有界域上-△u=λu的数值特征值外推法的研究  

The Probe into Extrapolation of Numerical Eigenvalue for -△u=λu on a Bounded Domain with Smooth Curve Boundary

作　　者：蔡惠[1] 何文明[1] 

机构地区：[1]温州大学数学与信息科学学院,浙江温州325035

出　　处：《温州大学学报（自然科学版）》2015年第4期1-7,共7页Journal of Wenzhou University(Natural Science Edition)

摘　　要：主要讨论在外推技术下,域Ω(QR^2,是具有光滑曲线边界的有界域)内-△u=λu特征值的超收敛性.在区域内部采用拟一致的矩形剖分,边界的曲边四边形则剖分成两个三角形(其中一个三角形的一条边是曲边),进而得到一种尺寸为h的特殊的剖分τ_h,在此基础上,在区域内部采用双线性元,在边界采用线性元,提出一种数值模拟该方程的有限元方法.利用外推技术发现,对于特征值来说,该有限元方法具有O(h^3)的超收敛性.This paper chiefly discusses the superconvergence of eigenvalue extrapolation technique for-△ u = λu(ΩR^2 is a bounded domain with a curved smooth boundary),where Ω is the solution domain.In the interior of domain,we use a quasi-uniform family of rectangular partitions,and on the boundary,we split any curved quadrangle into two triangles and one of which has one edge replaced by a segment of the boundary.By virtue of it,we present a special family of partitions τ_h with grid size h.Then,using the bi-linear element in the interior and a special element on the boundary,we present a special finite element method to solve-△u = λu over τ_h.By means of extrapolation technique,the superconvergence of the finite element method is figured out and the O(h^3) convergence rate is obtained.

关 键 词：超收敛性 特征值外推法 双线性元 

分 类 号：O241.82[理学—计算数学]