@Article{JCM-34-549, author = {Chen , GangFeng , Minfu and Xie , Xiaoping}, title = {Robust Globally Divergence-Free Weak Galerkin Methods for Stokes Equations}, journal = {Journal of Computational Mathematics}, year = {2016}, volume = {34}, number = {5}, pages = {549--572}, abstract = {

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 $P_k/P_{k-1} (k ≥ 1)$ 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1604-m2015-0447}, url = {http://global-sci.org/intro/article_detail/jcm/9812.html} }