TY - JOUR
T1 - Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations
AU - Chen , Gang
AU - Feng , Minfu
AU - Xie , Xiaoping
JO - Journal of Computational Mathematics
VL - 5
SP - 549
EP - 572
PY - 2016
DA - 2016/10
SN - 34
DO - http://doi.org/10.4208/jcm.1604-m2015-0447
UR - https://global-sci.org/intro/article_detail/jcm/9812.html
KW - Stokes equations, Weak Galerkin, Globally divergence-free, Uniform error
estimates, Local elimination.
AB - <p style="text-align: justify;">This paper proposes and analyzes a class of robust globally divergence-free weak Galerkin (WG) finite element methods for Stokes equations. The new methods use the $P_k/P_{k-1}&nbsp;(k ≥ 1)$ discontinuous finite element combination for velocity and pressure in the interior of elements, and piecewise $P_l/P_k (l=k-1,k)$ for the trace approximations of the velocity and pressure on the inter-element boundaries. Our methods not only yield globally divergence-free velocity solutions, but also have uniform error estimates with respect to the Reynolds number. Numerical experiments are provided to show the robustness of the proposed methods.</p>