In this work, the weak Galerkin finite element method (WG-FEM) is challenged by choosing a combination of the lowest degree of polynomial space for second-order elliptic problems. In this new scheme, we use the new stabilizer term. This scheme features piecewise-constant in each element T and piecewise-constant on \(\partial T\). The piecewise-constant weak Galerkin (PC-WG) scheme achieves O(h) and \(O(h^2)\) convergence in the \(H^1\) and \(L^2\) norms, respectively. The presented numerical results confirm the strength, flexibility and efficiency of our proposed scheme.

中文翻译：

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二阶问题的新$$ P_0 $$ P 0弱Galerkin有限元格式

在这项工作中，通过为二阶椭圆问题选择最低多项式空间的组合，对弱Galerkin有限元方法（WG-FEM）提出了挑战。在这个新方案中，我们使用新的稳定器术语。该方案在每个元素T中具有分段常数，而在\（\ partial T \）上具有分段常数。分段常数弱Galerkin（PC-WG）方案分别在\（H ^ 1 \）和\（L ^ 2 \）范数下实现O（h）和\（O（h ^ 2）\）收敛。给出的数值结果证实了我们提出的方案的强度，灵活性和效率。