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Superconvergence of the Crouzeix-Raviart element for elliptic equation

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Abstract

In this paper, a superconvergence result of the Crouzeix-Raviart element method is derived for the second-order elliptic equation on the uniform triangular meshes, in which any two adjacent triangles form a parallelogram. A local weighted averaging post-processing algorithm for the numerical stress is presented. Based on the equivalence between the Crouzeix-Raviart element method and the lowest order Raviart-Thomas element method, we prove that the error between the exact stress and the postprocessed numerical stress is of order h3/2. Two numerical examples are presented to confirm the theoretical result.

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Funding

Huang’s reserach was partially supported by NSFC Project (11826212) and Project of Scientific Research Fund of Hunan Provincial Science and Technology Department (2018WK4006). Yi’s reserach was partially supported by NSFC Project (11671341), Hunan Provincial NSF Project (2019JJ20016), and Department of Education of Hunan Province Project (16A206).

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Authors and Affiliations

  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, 411105, People’s Republic of China

    Yidan Zhang, Yunqing Huang & Nianyu Yi

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, People’s Republic of China

    Yidan Zhang, Yunqing Huang & Nianyu Yi

Authors
  1. Yidan Zhang
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  2. Yunqing Huang
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  3. Nianyu Yi
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Correspondence to Nianyu Yi.

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Communicated by: Paul Houston

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Zhang, Y., Huang, Y. & Yi, N. Superconvergence of the Crouzeix-Raviart element for elliptic equation. Adv Comput Math 45, 2833–2844 (2019). https://doi.org/10.1007/s10444-019-09714-9

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