TY - JOUR
T1 - New Error Estimates for Linear Triangle Finite Elements in the Steklov Eigenvalue Problem
AU - Bi , Hai
AU - Yang , Yidu
AU - Yu , Yuanyuan
AU - Han , Jiayu
JO - Journal of Computational Mathematics
VL - 5
SP - 682
EP - 692
PY - 2018
DA - 2018/06
SN - 36
DO - http://doi.org/10.4208/jcm.1703-m2014-0188
UR - https://global-sci.org/intro/article_detail/jcm/12452.html
KW - Steklov eigenvalue problem, Concave polygonal domain, Linear conforming
finite element, Nonconforming Crouzeix-Raviart element, Error estimates.
AB - <p style="text-align: justify;">This paper is concerned with the finite elements approximation for the Steklov eigenvalue
problem on concave polygonal domain. We make full use of the regularity estimate
and the characteristic of edge average interpolation operator of nonconforming Crouzeix-Raviart&nbsp;element, and prove a new and optimal error estimate in&nbsp;$‖·‖_{0,∂Ω}$ for the eigenfunction
of linear conforming finite element and the nonconforming Crouzeix-Raviart element.
Finally, we present some numerical results to support the theoretical analysis.</p>