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Gradient Recovery for the Crouzeix–Raviart Element

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Abstract

A gradient recovery method for the Crouzeix–Raviart element is proposed and analyzed. The proposed method is based on local discrete least square fittings. It is proven to preserve quadratic polynomials and be a bounded linear operator. Numerical examples indicate that it can produce a superconvergent gradient approximation for both elliptic equations and Stokes equations. In addition, it provides an asymptotically exact posteriori error estimators for the Crouzeix–Raviart element.

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Authors and Affiliations

  1. Department of Mathematics, Wayne State University, Detroit, MI, 48202, USA

    Hailong Guo & Zhimin Zhang

  2. Beijing Computational Science Research Center, Beijing, 100084, China

    Zhimin Zhang

Authors
  1. Hailong Guo
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  2. Zhimin Zhang
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Correspondence to Hailong Guo.

Additional information

This work is supported in part by the US National Science Foundation through Grants DMS-1115530 and DMS-1419040 and National Natural Science Foundation of China under Grants 91430216 and 11471031.

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Guo, H., Zhang, Z. Gradient Recovery for the Crouzeix–Raviart Element. J Sci Comput 64, 456–476 (2015). https://doi.org/10.1007/s10915-014-9939-5

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  • DOI: https://doi.org/10.1007/s10915-014-9939-5

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