Finite element approximation of the Neumann eigenvalue problem in domains with multiple cracks

被引：0
|
作者：
Belhachmi, Zakaria [1 ]
Bucur, Dorin [1 ]
Sac-Epee, Jean-Marc [1 ]
机构：
[1] Univ Metz Ile Saulcy, Dept Math, UMR 7122, CNRS, F-57045 Metz 01, France
来源：
IMA JOURNAL OF NUMERICAL ANALYSIS | 2006年 / 26卷 / 04期
关键词：
eigenvalues; Neumann-Laplacian; domains with cracks; finite elements method;
D O I：
10.1093/imanum/drl002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the Neumann-Laplacian eigenvalue problem in domains with multiple cracks. We derive a mixed variational formulation which holds on the whole geometric domain (including the cracks) and implements efficient finite-element discretizations for the computation of eigenvalues. Optimal error estimates are given and several numerical examples are presented, confirming the efficiency of the method. As applications, we numerically investigate the behaviour of the low eigenvalues in domains with a large number of cracks.
引用
收藏
页码：790 / 810
页数：21
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