@Article{CiCP-26-160,
author = {Qilong Zhai, Hehu Xie, Ran Zhang and Zhimin Zhang},
title = {The Weak Galerkin Method for Elliptic Eigenvalue Problems},
journal = {Communications in Computational Physics},
year = {2019},
volume = {26},
number = {1},
pages = {160--191},
abstract = {<p style="text-align: justify;">This article is devoted to studying the application of the weak Galerkin
(WG) finite element method to the elliptic eigenvalue problem with an emphasis on
obtaining lower bounds. The WG method uses discontinuous polynomials on polygonal or polyhedral finite element partitions. The non-conforming finite element space of
the WG method is the key of the lower bound property. It also makes the WG method
more robust and flexible in solving eigenvalue problems. We demonstrate that the WG
method can achieve arbitrary high convergence order. This is in contrast with existing
nonconforming finite element methods which can provide lower bound approximations by linear finite elements. Numerical results are presented to demonstrate the
efficiency and accuracy of the theoretical results.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2018-0201},
url = {http://global-sci.org/intro/article_detail/cicp/13030.html}
}