TY - JOUR
T1 - Numerical Investigation on Weak Galerkin Finite Elements
AU - Wang , Junping
AU - Ye , Xiu
AU - Zhang , Shangyou
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 517
EP - 531
PY - 2020
DA - 2020/08
SN - 17
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/17867.html
KW - Weak Galerkin, finite element methods, weak gradient, second-order elliptic problems, stabilizer-free.
AB - <p style="text-align: justify;">The weak Galerkin (WG) finite element method is an effective and robust numerical technique for the approximate solution of partial differential equations. The essence of the
method is the use of weak finite element functions and their weak derivatives computed with a
framework that mimics the distribution or generalized functions. Weak functions and their weak
derivatives can be constructed by using polynomials of arbitrary degrees; each chosen combination
of polynomial subspaces generates a particular set of weak Galerkin finite elements in application
to PDE solving. This article explores the computational performance of various weak Galerkin
finite elements in terms of stability, convergence, and supercloseness when applied to the model
Dirichlet boundary value problem for a second order elliptic equation. The numerical results are
illustrated in 31 tables, which serve two purposes: (1) they provide detailed and specific guidance
on the numerical performance of a large class of WG elements, and (2) the information shown in
the tables may open new research projects for interested researchers as they interpret the results
from their own perspectives.</p>