Recently, a new stabilizer free weak Galerkin method (SFWG) is proposed, which is easier to implement and more efficient. The main idea is that by letting $j\geq j_{0}$ for some $j_{0}$, where $j$ is the degree of the polynomials used to compute the weak gradients, then the stabilizer term in the regular weak Galerkin method is no longer needed. Later on in \cite{al2019note}, the optimal of such $j_{0}$ for certain types of finite element spaces was given. In this paper, we propose a new efficient SFWG scheme using the lowest possible orders of piecewise polynomials for triangular meshes in $2 D$ with the optimal order of convergence.

中文翻译：

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无最低阶稳定器的弱伽辽金有限元方法

最近，提出了一种新的无稳定剂弱伽辽金方法（SFWG），它更容易实现且更有效。主要思想是通过让 $j\geq j_{0}$ 代表某些 $j_{0}$，其中 $j$ 是用于计算弱梯度的多项式的次数，然后是常规弱梯度中的稳定项不再需要伽辽金法。后来在 \cite{al2019note} 中，给出了对于某些类型的有限元空间的此类 $j_{0}$ 的最优值。在本文中，我们提出了一种新的高效 SFWG 方案，它使用 $2 D$ 中三角形网格的分段多项式的最低可能阶次，并具有最佳收敛阶次。