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

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 nons...

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Veröffentlicht in:	Journal of scientific computing Jg. 89; H. 1; S. 8
Hauptverfasser:	Han, Weimin, Czuprynski, Kenneth, Jing, Feifei
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.10.2021 Springer Nature B.V
Schlagworte:	Algorithms Banach spaces Boundary conditions Computational Mathematics and Numerical Analysis Error analysis Finite element analysis Finite element method Flow velocity Fluid flow Incompressibility Incompressible flow Incompressible fluids Inequality Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Navier-Stokes equations Theoretical Navier–Stokes equations Hemivariational inequality Mixed finite element method 47J20 Error estimation Uniqueness 76D05 Existence 65N30
ISSN:	0885-7474, 1573-7691
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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.
AbstractList	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.
ArticleNumber	8
Author	Jing, Feifei Czuprynski, Kenneth Han, Weimin
Author_xml	– sequence: 1 givenname: Weimin surname: Han fullname: Han, Weimin organization: Department of Mathematics, University of Iowa – sequence: 2 givenname: Kenneth surname: Czuprynski fullname: Czuprynski, Kenneth organization: Program in Applied Mathematical and Computational Sciences (AMCS), University of Iowa – sequence: 3 givenname: Feifei orcidid: 0000-0002-7811-1443 surname: Jing fullname: Jing, Feifei email: ffjing@nwpu.edu.cn organization: School of Mathematics and Statistics and Xi’an Key Laboratory of Scientific Computation and Applied Statistics, Northwestern Polytechnical University
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Keywords	Navier–Stokes equations Hemivariational inequality Mixed finite element method 47J20 Error estimation Uniqueness 76D05 Existence 65N30
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Snippet	In this paper, we develop and study the mixed finite element method for a hemivariational inequality of the stationary Navier–Stokes equations (NS...
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SubjectTerms	Algorithms Banach spaces Boundary conditions Computational Mathematics and Numerical Analysis Error analysis Finite element analysis Finite element method Flow velocity Fluid flow Incompressibility Incompressible flow Incompressible fluids Inequality Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Navier-Stokes equations Theoretical
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Title	Mixed Finite Element Method for a Hemivariational Inequality of Stationary Navier–Stokes Equations
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