TY - JOUR
T1 - A Posteriori Error Estimator for a Weak Galerkin Finite Element Solution of the Stokes Problem
AU - Xiaobo Zheng & Xiaoping Xie
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 508
EP - 529
PY - 2018
DA - 2018/02
SN - 7
DO - http://doi.org/10.4208/eajam.221216.250417a
UR - https://global-sci.org/intro/article_detail/eajam/10762.html
KW - The Stokes equations, weak Galerkin method, a posteriori error estimator.
AB - <p style="text-align: justify;">A robust residual-based a posteriori error estimator is proposed for a weak
Galerkin finite element method for the Stokes problem in two and three dimensions.
The estimator consists of two terms, where the first term characterises the difference
between the $L^2$-projection of the velocity approximation on the element interfaces and
the corresponding numerical trace, and the second is related to the jump of the velocity
approximation between the adjacent elements. We show that the estimator is reliable
and efficient through two estimates of global upper and global lower bounds, up to two
data oscillation terms caused by the source term and the nonhomogeneous Dirichlet
boundary condition. The estimator is also robust in the sense that the constant factors
in the upper and lower bounds are independent of the viscosity coefficient. Numerical
results are provided to verify the theoretical results.</p>