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Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method

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Abstract

Superconvergence and recovery type a posteriori error estimators are analyzed for Pian and Sumihara’s 4-node hybrid stress quadrilateral finite element method for linear elasticity problems. Superconvergence of order O(h 1+min{α,1}) is established for both the displacement approximation in H 1-norm and the stress approximation in L 2-norm under a mesh assumption, where α > 0 is a parameter characterizing the distortion of meshes from parallelograms to quadrilaterals. Recovery type approximations for the displacement gradients and the stress tensor are constructed, and a posteriori error estimators based on the recovered quantities are shown to be asymptotically exact. Numerical experiments confirm the theoretical results.

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Authors and Affiliations

  1. College of Sciences, Southwest Petroleum University, Chengdu, 610500, China

    YanHong Bai

  2. School of Mathematics, Sichuan University, Chengdu, 610064, China

    YanHong Bai & XiaoPing Xie

  3. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, China

    YongKe Wu

Authors
  1. YanHong Bai
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  2. YongKe Wu
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  3. XiaoPing Xie
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Correspondence to XiaoPing Xie.

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Bai, Y., Wu, Y. & Xie, X. Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method. Sci. China Math. 59, 1835–1850 (2016). https://doi.org/10.1007/s11425-016-5144-3

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  • DOI: https://doi.org/10.1007/s11425-016-5144-3

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