Finite element method for a stationary Stokes hemivariational inequality with slip boundary condition

Changjie Fang, Kenneth Czuprynski, Weimin Han, Xiaoliang Cheng, Xiaoxia Dai

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    3 Scopus citations

    Abstract

    This paper is devoted to the study of a hemivariational inequality problem for the stationary Stokes equations with a nonlinear slip boundary condition. The hemivariational inequality is formulated with the use of the generalized directional derivative and generalized gradient in the sense of Clarke. We provide an existence and uniqueness result for the hemivariational inequality. Then we apply the finite element method to solve the hemivariational inequality. The incompressibility constraint is treated through a mixed formulation. Error estimates are derived for numerical solutions. Numerical simulation results are reported to illustrate the theoretically predicted convergence orders.

    Original languageEnglish (US)
    Pages (from-to)2696-2716
    Number of pages21
    JournalIMA Journal of Numerical Analysis
    Volume40
    Issue number4
    DOIs
    StatePublished - 2020

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)
    • Computational Mathematics
    • Applied Mathematics

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