@article{XU2024, 
author = {Liangkun XU and Hai BI},
title = {A Posteriori Error Estimation of Adaptive Multigrid Method for Steklov-Lamé Eigenproblem},
year = {2024},
journal = {Journal of Xinjiang University(Natural Science Edition in Chinese and English)},
volume = {41},
number = {2},
pages = {157-170,180},
keywords = {Steklov-Lamé eigenvalues, multigrid discretization based on shifted inverse iteration, a posteriori error estimation, adaptive multigrid algorithm},
url = {https://www.sciopen.com/article/10.13568/j.cnki.651094.651316.2023.12.24.0002},
doi = {10.13568/j.cnki.651094.651316.2023.12.24.0002},
abstract = {We establish a finite element multigrid discretization scheme based on the shifted-inverse iteration for the Steklov-Lamé 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 L2(∂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-Lamé eigenproblem.}
}