A weak Galerkin (WG) finite element method without stabilizers was introduced in Ye and Zhang (2020) on polytopal mesh. Then it was improved in Ye and Zhang (2021) 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.

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：第三部分

Ye and Zhang（2020）在多边网格上引入了一种不带稳定剂的弱Galerkin（WG）有限元方法。然后在Ye和Zhang（2021）中以一阶超收敛进行了改进。本文的目的是开发一种新的无稳定剂的多面体网格WG方法。在能量范数和能量范式中，该方法的收敛速度均比相应WG解决方案的最优收敛速度高两个数量级。${\mathrm{大号}}^{\mathrm{2个}}$规范。数值示例针对二维和三维空间中的低阶和高阶元素进行了测试。