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 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.

中文翻译：

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多面体网格上的无稳定剂弱Galerkin有限元方法：第二部分

本文的第一部分介绍了一种基于多稳定网格的无稳定剂弱Galerkin（WG）有限元方法（Ye and Zhang（2020））。从不连续的有限元方法中删除稳定剂可以简化公式并降低编程复杂性。本文的目的是介绍一种新的不带稳定剂的WG方法，该方法在收敛性上比最优收敛性高一个数量级。此方法是在多形网格上实现超收敛的第一个WG方法。给出了2D和3D中的数值示例，证明了该定理。