TY - JOUR
T1 - A Weak Galerkin Mixed Finite Element Method for Second-Order Elliptic Equations with Robin Boundary Conditions
AU - Zhang , Qian
AU - Zhang , Ran
JO - Journal of Computational Mathematics
VL - 5
SP - 532
EP - 548
PY - 2016
DA - 2016/10
SN - 34
DO - http://doi.org/10.4208/jcm.1604-m2015-0413
UR - https://global-sci.org/intro/article_detail/jcm/9811.html
KW - Second-order elliptic equations, Robin boundary conditions, Weak Galerkin,
Weak divergence.
AB - <p style="text-align: justify;">In this paper, we present a weak Galerkin (WG) mixed finite element method for solving the second-order elliptic equations with Robin boundary conditions. Stability and a priori error estimates for the coupled method are derived. We present the optimal order error estimate for the WG-MFEM approximations in a norm that is related to the $L^2$ for the flux and $H^1$ for the scalar function. Also an optimal order error estimate in $L^2$ is derived for the scalar approximation by using a duality argument. A series of numerical experiments is presented that verify our theoretical results.</p>