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

Weimin Han, Kenneth Czuprynski, Feifei Jing

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    1 Scopus citations

    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.

    Original languageEnglish (US)
    Article number8
    JournalJournal of Scientific Computing
    Volume89
    Issue number1
    DOIs
    StatePublished - Oct 2021

    All Science Journal Classification (ASJC) codes

    • Software
    • Theoretical Computer Science
    • Numerical Analysis
    • Engineering(all)
    • Computational Theory and Mathematics
    • Computational Mathematics
    • Applied Mathematics

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