  A discrete divergence-free weak Galerkin finite element method is developed
for the Stokes equations based on a weak Galerkin (WG) method introduced in the
reference [15]. Discrete divergence-free bases are constructed explicitly for
the lowest order weak Galerkin elements in two and three dimensional spaces.
These basis functions can be derived on general meshes of arbitrary shape of
polygons and polyhedrons. With the divergence-free basis derived, the discrete
divergence-free WG scheme can eliminate the pressure variable from the system
and reduces a saddle point problem to a symmetric and positive definite system
with many fewer unknowns. Numerical results are presented to demonstrate the
robustness and accuracy of this discrete divergence-free WG method.
