The local superconvergence of the linear finite element method for the poisson problem |
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| Authors: | Wen‐ming He Jun‐Zhi Cui Qi‐ding Zhu Zhong‐liang Wen |
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| Affiliation: | 1. Department of Mathematics, Wenzhou University, , Wenzhou, Zhejiang, 325035 People's Republic of China;2. LSEC, , Beijing 100190, China;3. College of Mathematics and Computer Science, Hunan Normal University, , Changsha 410081, China |
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| Abstract: | Assume that  . In this study, the Richardson extrapolation for the tensor‐product block element and the linear finite element theory of the Green's function will be combined to study the local superconvergence of finite element methods for the Poisson equation in a bounded polytopic domain (polygonal or polyhedral domain for ), where a family of tensor‐product block partitions is not required or the solution need not have high global smoothness. We present a special family of partitions satisfying, for any , e is a tensor‐product block whenever where denotes the distance between e and . By the linear finite element theory of the Green's function and the Richardson extrapolation for the tensor‐product block element, we obtain the local superconvergence of the displacement for the linear finite element method over the special family of partitions . © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 930–946, 2014 |
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| Keywords: | displacement Green's function local superconvergence Richardson extrapolation tensor‐product block |
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