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Local and parallel finite element methods for the coupled Stokes/Darcy model

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Abstract

In this paper, based on two-grid discretizations, two kinds of local and parallel finite element methods are proposed and investigated for the coupled Stokes/Darcy model. Following the idea presented in Xu and Zhou (Math. Comput. 69, 881–909 1999). a classical local and parallel finite element method is proposed and investigated. To derive global continuous approximations, a new local and parallel finite element method is devised by combining the partition of unity. We theoretically analyze the resulting formulations and derive optimal error estimates. Numerical experiments are reported to assess the theoretical results.

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Funding

This work is subsidized by NSFC(Grant No.11701343, 11801332) and Natural Science Foundation of Shandong Province (Grant No. ZR2017BA027, ZR2019BA002).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Guangzhi Du

  2. School of Mathematical Sciences, University of Jinan, Jinan, 250022, China

    Liyun Zuo

Authors
  1. Guangzhi Du
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  2. Liyun Zuo
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Correspondence to Guangzhi Du.

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Du, G., Zuo, L. Local and parallel finite element methods for the coupled Stokes/Darcy model. Numer Algor 87, 1593–1611 (2021). https://doi.org/10.1007/s11075-020-01021-5

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  • DOI: https://doi.org/10.1007/s11075-020-01021-5

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