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A numerical method for solving three-dimensional elliptic interface problems with triple junction points

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Abstract

Elliptic interface problems with multi-domains have wide applications in engineering and science. However, it is challenging for most existing methods to solve three-dimensional elliptic interface problems with multi-domains due to local geometric complexity, especially for problems with matrix coefficient and sharp-edged interface. There are some recent work in two dimensions for multi-domains and in three dimensions for two domains. However, the extension to three dimensional multi-domain elliptic interface problems is non-trivial. In this paper, we present an efficient non-traditional finite element method with non-body-fitting grids for three-dimensional elliptic interface problems with multi-domains. Numerical experiments show that this method achieves close to second order accurate in the L ∞ norm for piecewise smooth solutions.

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Acknowledgments

We thank the reviewers for their effort helping us to improve the manuscript. L. Shi’s research is supported by Science Foundations of China University of Political Science and Law [Grant numbers 1000-10816106 and 1000-10816330]. S. Hou’s research is supported by National Science Foundation [Grant number DMS-1317994] and Dr. Walter Koss Professorship. L. Wang’s research is supported by Science Foundations of China University of Petroleum–Beijing [Grant numbers 2462015BJB05, 2462015YQ0604 and 2462015QZDX02].

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Authors and Affiliations

  1. Department of Mathematics, College of Science, China University of Petroleum-Beijing, Beijing, 102249, China

    Liqun Wang

  2. Department of Mathematics and Statistics, Louisiana Tech University, Ruston, LA, 71272, USA

    Songming Hou

  3. Department of Science and Technology Teaching, China University of Political Science and Law, Beijing, 102249, China

    Liwei Shi

Authors
  1. Liqun Wang
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  2. Songming Hou
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  3. Liwei Shi
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Correspondence to Liwei Shi.

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Communicated by: John Lowengrub

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Wang, L., Hou, S. & Shi, L. A numerical method for solving three-dimensional elliptic interface problems with triple junction points. Adv Comput Math 44, 175–193 (2018). https://doi.org/10.1007/s10444-017-9539-7

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  • DOI: https://doi.org/10.1007/s10444-017-9539-7

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