  A weak Galerkin (WG) finite element method without stabilizers was introduced
in [J. Comput. Appl. Math., 371 (2020). arXiv:1906.06634] on polytopal mesh.
Then it was improved in [arXiv:2008.13631] with order one superconvergence. The
goal of this paper is to develop a new stabilizer free WG method on polytopal
mesh. This method has convergence rates two orders higher than the optimal
convergence rates for the corresponding WG solution in both an energy norm and
the $L^2$ norm. The numerical examples are tested for low and high order
elements in two and three dimensional spaces.
