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A New Numerical Method for an Asymptotic Coupled Model of Fractured Media Aquifer System

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Abstract

An asymptotic model coupling three-dimensional and two-dimensional equations is considered to demonstrate the flow in fractured media aquifer system in this paper. The flow is governed by Darcy’s law both in fractures and surrounding porous media. A new anisotropic and nonconforming finite element is constructed to solve the three-dimensional Darcy equation. The existence and uniqueness of the coupled solutions are deduced. Optimal error estimates are obtained in \(L^2\) and \(H^1\) norms. Numerical experiments show the accuracy and efficiency of the presented method. With the same number of nodal points and the same amount of computational costs, the results obtained by using the new element are much better than those by both \(Q_{1}\) conforming element and Wilson nonconforming element on the same meshes.

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Authors and Affiliations

  1. School of Mathematics and Statistics Science, Ludong University, Yantai, 264025, China

    Wei Liu

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong

    Jintao Cui

  3. The Hong Kong Polytechnic University Shenzhen Research Institute, Shenzhen, 518057, China

    Jintao Cui

  4. School of Mathematics and Information Sciences, Yantai University, Yantai, 264005, China

    Zhifeng Wang

Authors
  1. Wei Liu
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  2. Jintao Cui
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  3. Zhifeng Wang
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Correspondence to Jintao Cui.

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The work of Wei Liu was supported by Shandong Provincial Natural Science Foundation No. ZR2019MA049 and in part by The Hong Kong Polytechnic University AMSS-PolyU Joint Research Institute (JRI) 1-ZVA8. Jintao Cui’s research is supported in part by the Hong Kong RGC, General Research Fund (GRF) Grant No. 15302518 and the National Natural Science Foundation of China (NSFC) Grant No. 11771367.

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Liu, W., Cui, J. & Wang, Z. A New Numerical Method for an Asymptotic Coupled Model of Fractured Media Aquifer System. J Sci Comput 82, 9 (2020). https://doi.org/10.1007/s10915-019-01112-z

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  • DOI: https://doi.org/10.1007/s10915-019-01112-z

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