  A weak Galerkin (WG) finite element method for solving the stationary Stokes
equations in two- or three- dimensional spaces by using discontinuous piecewise
polynomials is developed and analyzed. The variational form we considered is
based on two gradient operators which is different from the usual
gradient-divergence operators. The WG method is highly flexible by allowing the
use of discontinuous functions on arbitrary polygons or polyhedra with certain
shape regularity. Optimal-order error estimates are established for the
corresponding WG finite element solutions in various norms. Numerical results
are presented to illustrate the theoretical analysis of the new WG finite
element scheme for Stokes problems.

Numerical Analysis