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 ∂T. The piecewise-constant weak Galerkin (PC-WG) scheme achieves O(h) and O(h2) convergence in the H1 and L2 norms, respectively. The presented numerical results confirm the strength, flexibility and efficiency of our proposed scheme.
