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The Nonconforming Virtual Element Method for a Stationary Stokes Hemivariational Inequality with Slip Boundary Condition

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Abstract

In this paper, the nonconforming virtual element method is studied to solve a hemivariational inequality problem for the stationary Stokes equations with a nonlinear slip boundary condition. The nonconforming virtual elements enriched with polynomials on slip boundary are used to discretize the velocity, and discontinuous piecewise polynomials are used to approximate the pressure. The inf-sup condition is shown for the nonconforming virtual element method. An error estimate is derived under appropriate solution regularity assumptions, and the error bound is of optimal order when lowest-order virtual elements for the velocity and piecewise constants for the pressure are used. A numerical example is presented to illustrate the theoretically predicted convergence order.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Min Ling & Weimin Han

  2. School of Mathematics and Statistics and State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, China

    Fei Wang

  3. Department of Mathematics and Program in Applied Mathematical and Computational Sciences, University of Iowa, Iowa City, IA, 52242, USA

    Weimin Han

Authors
  1. Min Ling
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  2. Fei Wang
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  3. Weimin Han
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Correspondence to Fei Wang.

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The work of this author was partially supported by the National Natural Science Foundation of China (Grant No. 11771350).

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Ling, M., Wang, F. & Han, W. The Nonconforming Virtual Element Method for a Stationary Stokes Hemivariational Inequality with Slip Boundary Condition. J Sci Comput 85, 56 (2020). https://doi.org/10.1007/s10915-020-01333-7

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  • DOI: https://doi.org/10.1007/s10915-020-01333-7

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