Guaranteed Lower Eigenvalue Bounds for Steklov Operators Using Conforming Finite Element Methods

被引：3
|
作者：
Nakano, Taiga [2 ]
Li, Qin [3 ]
Yue, Meiling [3 ]
Liu, Xuefeng [1 ]
机构：
[1] Niigata Univ, Fac Sci, 8050 Ikarashi 2 Cho,Nishi Ku, Niigata, Niigata 9502181, Japan
[2] Niigata Univ, Grad Sch Sci & Technol, 8050 Ikarashi 2 Cho,Nishi Ku, Niigata, Niigata 9502181, Japan
[3] Beijing Technol & Business Univ, Sch Math & Stat, Beijing 100048, Peoples R China
来源：
COMPUTATIONAL METHODS IN APPLIED MATHEMATICS | 2024年 / 24卷 / 02期
基金：
中国国家自然科学基金; 日本学术振兴会;
关键词：
Steklov Eigenvalue Problems; Non-Homogeneous Neumann Problems; Finite Element Methods; Hypercircle; Guaranteed Lower Eigenvalue Bounds; A-POSTERIORI BOUNDS; LAPLACE EIGENVALUES; APPROXIMATIONS; EIGENVECTORS;
D O I：
10.1515/cmam-2022-0218
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For the eigenvalue problem of the Steklov differential operator, an algorithm based on the conforming finite element method (FEM) is proposed to provide guaranteed lower bounds for the eigenvalues. The proposed lower eigenvalue bounds utilize the a priori error estimation for FEM solutions to non-homogeneous Neumann boundary value problems, which is obtained by constructing the hypercircle for the corresponding FEM spaces and boundary conditions. Numerical examples demonstrate the efficiency of our proposed method.
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页码：487 / 502
页数：16
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