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A virtual element method for the coupled Stokes–Darcy problem with the Beaver–Joseph–Saffman interface condition

  • Xin Liu
  • Rui Li
  • Zhangxin ChenEmail author
Article
  • 80 Downloads

Abstract

In this work, we propose a virtual element method for discretizing the equations that couple the incompressible steady Stokes flow with the Darcy flow by means of the Beaver–Joseph–Saffman condition on their interface. In addition to avoiding explicit expressions of basis functions, this method can not only improve the computational efficiency of any polynomial degree, but also can treat any polygonal elements, including non-convex and non-matching elements. Moreover, combining with the discrete inf-sup condition of a virtual element approximation for the velocity and pressure pair \(P_{k}/P_{k-1}\), we can obtain optimal error estimates. Furthermore, numerical experiments are presented to show the efficiency and validity of the coupled method.

Keywords

Virtual element method Coupled Stokes–Darcy Beavers–Joseph–Saffman interface condition Any polynomial degree Polygonal meshes Non-matching elements 

Mathematics Subject Classification

65N30 65N12 65N15 76D07 76S05 

Notes

Acknowledgements

This work is supported by Fundamental Research Funds for the Central Universities of China (No.310201911qd001) and National Natural Science Foundation of China (No.11901462). This work is supported by Fundamental Research Funds for the Central Universities of China (No.GK201903007), National Natural Science Foundation of China (No.11901372), and Natural Science Foundation of Shaanxi Province (No.2019JQ-077).

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Copyright information

© Istituto di Informatica e Telematica (IIT) 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics, School of ScienceNorthwestern Polytechnical UniversityXi’anChina
  2. 2.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina
  3. 3.Department of Chemical and Petroleum EngineeringSchulich School of Engineering, University of CalgaryCalgaryCanada
  4. 4.College of Petroleum EngineeringChina University of PetroleumBeijingChina

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