  A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh
has been introduced in Part I of this paper (J. Comput. Appl. Math, 371 (2020)
112699. arXiv:1906.06634.) Removing stabilizers from discontinuous finite
element methods simplifies formulations and reduces programming complexity. The
purpose of this paper is to introduce a new WG method without stabilizers on
polytopal mesh that has convergence rates one order higher than optimal
convergence rates. This method is the first WG method that achieves
superconvergence on polytopal mesh. Numerical examples in 2D and 3D are
presented verifying the theorem.
