TY - JOUR
T1 - A Weak Galerkin Finite Element Method for the Elliptic Variational Inequality
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 923
EP - 941
PY - 2019
DA - 2019/04
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2018-0124
UR - https://global-sci.org/intro/article_detail/nmtma/13137.html
KW - Obstacle problem, the second kind of elliptic variational inequality, weak Galerkin finite
element method, discrete weak gradient.
AB - <p style="text-align: justify;">In this paper, we discuss the weak Galerkin (WG) finite element method for
the obstacle problem and the second kind of the elliptic variational inequality. We use
piecewise linear functions to approximate the exact solutions. The WG schemes for the
first and the second kind of elliptic variational inequality are established and the well-posedness of the two schemes are proved. Furthermore, we can obtain the optimal order
estimates in $H$<sup>1</sup> norm. Finally, some numerical examples are presented to confirm the
theoretical analysis.</p>