TY - JOUR
T1 - Weak Galerkin Finite Element Methods on Polytopal Meshes
AU - Lin Mu, Junping Wang & Xiu Ye
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 31
EP - 53
PY - 2015
DA - 2015/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/477.html
KW - weak Galerkin, finite element methods, discrete gradient, second-order elliptic problems, polytopal meshes.
AB - <p style="text-align: justify;">This paper introduces a new weak Galerkin (WG) finite element method for second
order elliptic equations on polytopal meshes. This method, called WG-FEM, is designed by
using a discrete weak gradient operator applied to discontinuous piecewise polynomials on finite
element partitions of arbitrary polytopes with certain shape regularity. The paper explains how
the numerical schemes are designed and why they provide reliable numerical approximations for
the underlying partial differential equations. In particular, optimal order error estimates are
established for the corresponding WG-FEM approximations in both a discrete $H^1$ norm and the
standard $L^2$ norm. Numerical results are presented to demonstrate the robustness, reliability,
and accuracy of the WG-FEM. All the results are established for finite element partitions with
polytopes that are shape regular.</p>