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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Vydáno v:Journal of scientific computing Ročník 89; číslo 1; s. 8
Hlavní autoři: Han, Weimin, Czuprynski, Kenneth, Jing, Feifei
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.10.2021
Springer Nature B.V
Témata:
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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Popis
Shrnutí: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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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01614-9