TY - JOUR
T1 - Fully Computable Error Bounds for Eigenvalue Problem
AU - Hong , Qichen
AU - Xie , Hehu
AU - Yue , Meiling
AU - Zhang , Ning
JO - International Journal of Numerical Analysis and Modeling
VL - 1-2
SP - 260
EP - 276
PY - 2018
DA - 2018/01
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10567.html
KW - Eigenvalue problem, computable error estimate, guaranteed upper bound, guaranteed lower bound, complementary method.
AB - <p style="text-align: justify;">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.</p>