TY - JOUR
T1 - The Weak Galerkin Method for Elliptic Eigenvalue Problems
AU - Qilong Zhai, Hehu Xie, Ran Zhang & Zhimin Zhang
JO - Communications in Computational Physics
VL - 1
SP - 160
EP - 191
PY - 2019
DA - 2019/02
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0201
UR - https://global-sci.org/intro/article_detail/cicp/13030.html
KW - Weak Galerkin finite element method, elliptic eigenvalue problem, lower bounds,
error estimate.
AB - <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>