Abstract
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.
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Communicated by Abimael Loula.
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Charati, A.Y., Momeni, H. & Cheichan, M.S. A new \(P_0\) weak Galerkin finite element scheme for second-order problems. Comp. Appl. Math. 40, 138 (2021). https://doi.org/10.1007/s40314-021-01521-7
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DOI: https://doi.org/10.1007/s40314-021-01521-7