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Local superconvergence of the derivative for tensor-product block FEM

Authors

  • Wen-Ming He,

    Corresponding author
    1. Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, Zhejiang, People's Republic of China, 310027
    2. Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang, People's Republic of China, 325035
    • Department of Engineering Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, Zhejiang, People's Republic of China, 310027
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  • Wei-Qiu Chen,

    1. Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang, People's Republic of China, 325035
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  • Qi-Ding Zhu

    1. Department of Information and Computing Science, College of Mathematics and Computer Science, Hunan Normal University, Changsha, People's Republic of China, 410081
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Abstract

In this article, we shall discuss local superconvergence of the derivative for tensor-product block finite elements over uniform partition for three-dimensional Poisson's equation on the basis of Liu and Zhu (Numer Methods Partial Differential Eq 25 (2009) 999–1008). Assume that odd m ≥ 3, x0 is an inner locally symmetric point of uniform rectangular partition equation image and ρ(x0,Ω) means the distance between x0 and boundary Ω. Combining the symmetry technique (Wahlbin, Springer, 1995; Schatz, Sloan, and Wahlbin, SIAM J Numer Anal 33 (1996), 505–521; Schatz, Math Comput 67 (1998), 877–899) with weak estimates for tensor-product block finite elements of degree m ≥ 3 [see Liu and Zhu, Numer Methods Partial Differential Eq 25 (2009) 999–1008] and the finite element theory of Green function in 3 presented in this article, we propose the equation image convergence of the derivatives for tensor-product block finite elements of degree m ≥ 3 on x0. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 457–475, 2012

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