Fully Computable Error Bounds for Eigenvalue Problem
Numerical Analysis
2016-06-21 v2
Abstract
This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an asymptotically lower bound of the general eigenvalues. Furthermore, we also give a guaranteed upper bound of the error estimates for the first eigenfunction approximation and a guaranteed lower bound of the first eigenvalue based on computable error estimator. Some numerical examples are presented to validate the theoretical results deduced in this paper.
Cite
@article{arxiv.1601.01561,
title = {Fully Computable Error Bounds for Eigenvalue Problem},
author = {Hehu Xie and Meiling Yue and Ning Zhang},
journal= {arXiv preprint arXiv:1601.01561},
year = {2016}
}
Comments
21 pages, 11 figures. In this version, we obtain a sharper estimate for the eigenvalue approximations