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Some superconvergence results of high-degree finite element method for a second order elliptic equation with variable coefficients |
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| Authors: | Xiaofei Guan Mingxia Li Wenming He Zhengwu Jiang |
| Institution: | 1. Department of Mathematics, Tongji University, 200092, Shanghai, China 2. School of Science, China University of Geosciences (Beijing), 100083, Beijing, China 3. Department of Mathematics, Wenzhou University, 325035, Wenzhou, China 4. Key Laboratory of Advanced Civil Engineering Materials of Ministry of Education, Tongji University, 200092, Shanghai, China |
| Abstract: | In this paper, some superconvergence results of high-degree finite element method are obtained for solving a second order elliptic equation with variable coefficients on the inner locally symmetric mesh with respect to a point x 0 for triangular meshes. By using of the weak estimates and local symmetric technique, we obtain improved discretization errors of O(h p+1 |ln h|2) and O(h p+2 |ln h|2) when p (≥ 3) is odd and p (≥ 4) is even, respectively. Meanwhile, the results show that the combination of the weak estimates and local symmetric technique is also effective for superconvergence analysis of the second order elliptic equation with variable coefficients. |
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