The local superconvergence of the quadratic triangular element for the poisson problem in a polygonal domain |
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| Authors: | Wen‐Ming He Jun‐Zhi Cui Qi‐Ding Zhu |
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| Institution: | 1. Department of Mathematics, Wenzhou University, , Wenzhou, Zhejiang, 325035 People's Republic of China;2. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, , Beijing, 100190 China;3. Department of Mathematics, Hunan Normal University, , Changsha, 410081 China |
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| Abstract: | It is the first time for us to combine the local symmetric technique and the weak estimates to investigate the local superconvergence of the finite element method for the Poisson equation in a bounded domain with polygonal boundary where a uniform family of partitions is not required or the solution need not have high global smoothness. Combining a uniform family of triangulations in the interior of domain with a quasiuniform family of triangulations at the boundary of domain, we present a special family of triangulations. By the finite element theory of the derivative of the Green's function presented in this article, we combine the local symmetric technique and the weak estimates to obtain the local superconvergence of the derivative for the quadratic elements. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1854–1876, 2014 |
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| Keywords: | Poisson equation polygonal boundary the quadratic triangular element the local superconvergence the local symmetric technique the weak estimates |
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