Steklov-Lame特征值问题自适应多网格方法的后验误差估计  

A Posteriori Error Estimation of Adaptive Multigrid Method for Steklov-Lame Eigenproblem

作　　者：徐良坤 闭海 XU Liangkun;BI Hai(School of Mathematical Sciences,Guizhou Normal University,Guiyang Guizhou 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《新疆大学学报（自然科学版中英文）》2024年第2期157-170,180,共15页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：supported by the National Natural Science Foundation of the People’s Republic of China“The research of finite element methods for eigenvalue problems in inverse scattering”(12261024)。

摘　　要：建立Steklov-Lame特征值问题的一种基于移位反迭代的有限元多网格离散方案,并研究该方案基于残差型的后验误差估计.首先给出近似特征函数在L^(2)(∂Ω)范数意义下的误差估计,其次给出多网格方案近似解的后验误差指示子,并证明后验误差指示子的可靠性和有效性.最后利用后验误差指示子设计自适应多网格算法并用于求解Steklov-Lame特征值问题.We establish a finite element multigrid discretization scheme based on the shifted-inverse iteration for the Steklov-Lame eigenproblem,and investigate the a posteriori error estimation of residual type for the scheme.Firstly,we give the error estimation of the approximate eigenfunction in the sense of L^(2)(∂Ω)norm,then we give the a posteriori error indicators for the multigrid approximate solution,and prove the reliability and efficiency of the indicators.Finally,we use the a posteriori error indicators to design an adaptive multigrid algorithm for solving the Steklov-Lame eigenproblem.

关 键 词：Steklov-Lame特征值 基于移位反迭代的多网格离散 后验误差估计 自适应多网格算法 

分 类 号：O241.1[理学—计算数学]