  A stabilizing/penalty term is often used in finite element methods with
discontinuous approximations to enforce connection of discontinuous functions
across element boundaries. Removing stabilizers from discontinuous finite
element methods will simplify the formulations and reduce programming
complexity significantly. The goal of this paper is to introduce a stabilizer
free weak Galerkin finite element method for second order elliptic equations on
polytopal meshes in 2D or 3D. This new WG method keeps a simple symmetric
positive definite form and can work on polygonal/polyheral meshes. Optimal
order error estimates are established for the corresponding WG approximations
in both a discrete $H^1$ norm and the $L^2$ norm. Numerical results are
presented verifying the theorem.
