(untitled) (Journal of Computational Mathematics, 2018)
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.