Article history: Received 27 March 2011 Accepted 3 May 2012 Available online 15 May 2012

A weak Galerkin (WG) finite element method without stabilizers was introduced in Ye and Zhang (2020) on polytopal mesh. Then it improved (2021) with order one superconvergence. The goal of this paper is to develop a new stabilizer free WG This has convergence rates two orders higher than the optimal for corresponding solution both an energy norm L2 norm. numerical examples are tested low high e...

A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh has been introduced in Part I of this paper (Ye and Zhang (2020)). Removing stabilizers from discontinuous methods simplifies formulations reduces programming complexity. The purpose is to introduce a new WG without that convergence rates one order higher than optimal rates. This the first achieves superconvergence mes...