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The Superconvergent Cluster Recovery Method

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Abstract

A new gradient recovery technique SCR (Superconvergent Cluster Recovery) is proposed and analyzed for finite element methods. A linear polynomial approximation is obtained by a least-squares fitting to the finite element solution at certain sample points, which in turn gives the recovered gradient at recovering points. Compared with similar techniques such as SPR and PPR, our approach is cheaper and efficient, while having same or even better accuracy. In additional, it can be used as an a posteriori error estimator, which is relatively simple to implement, cheap in terms of storage and computational cost for adaptive algorithms. We present some numerical examples illustrating the effectiveness of our recovery procedure.

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Authors and Affiliations

  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, Hunan, P.R. China

    Yunqing Huang & Nianyu Yi

Authors
  1. Yunqing Huang
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  2. Nianyu Yi
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Correspondence to Yunqing Huang.

Additional information

The first author is supported by NSFC for Distinguished Young Scholar 10625106, and the National Basic Research Program of China under the grant 2005CB321701. The second author is supported by Graduate school visit project of Peking University and Hunan Provincial Innovation Foundation for Postgraduate (S2008yjscx05).

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Huang, Y., Yi, N. The Superconvergent Cluster Recovery Method. J Sci Comput 44, 301–322 (2010). https://doi.org/10.1007/s10915-010-9379-9

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  • DOI: https://doi.org/10.1007/s10915-010-9379-9

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