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Mixed Finite Element Method for a Hemivariational Inequality of Stationary Navier–Stokes Equations

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Abstract

In this paper, we develop and study the mixed finite element method for a hemivariational inequality of the stationary Navier–Stokes equations (NS hemivariational inequality). The NS hemivariational inequality models the motion of a viscous incompressible fluid in a bounded domain, subject to a nonsmooth and nonconvex slip boundary condition. The incompressibility contraint is treated through a mixed formulation. Solution existence and uniqueness are explored. The mixed finite element method is applied to solve the NS hemivariational inequality and error estimates are derived. Numerical results are reported on the use of the P1b/P1 pair, illustrating the optimal convergence order predicted by the error analysis.

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Authors and Affiliations

  1. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    Weimin Han

  2. Program in Applied Mathematical and Computational Sciences (AMCS), University of Iowa, Iowa City, IA, 52242, USA

    Kenneth Czuprynski

  3. School of Mathematics and Statistics and Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University, Xi’an, 710129, Shaanxi, China

    Feifei Jing

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  1. Weimin Han
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  3. Feifei Jing
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This work is supported by the National Natural Science Foundation of China (No. 12001413) and the Postdoctoral Science Foundation of China (No. 2021M692647).

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Han, W., Czuprynski, K. & Jing, F. Mixed Finite Element Method for a Hemivariational Inequality of Stationary Navier–Stokes Equations. J Sci Comput 89, 8 (2021). https://doi.org/10.1007/s10915-021-01614-9

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