On a Stokes hemivariational inequality for incompressible fluid flows with damping

In this paper, a Stokes hemivariational inequality is studied for incompressible fluid flows with the damping effect. The hemivariational inequality feature is caused by the presence of a nonsmooth slip boundary condition of friction type. Well-posedness of the Stokes hemivariational inequality is e...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications Vol. 79; p. 104131
Main Authors: Han, Weimin, Qiu, Hailong, Mei, Liquan
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.10.2024
Subjects:
Error estimation
Hemivariational inequality
Minimization principle
Mixed finite element method
Stokes equations with damping
Well-posedness
Hemivariational inequality
Mixed finite element method
Error estimation
Minimization principle
Stokes equations with damping
Well-posedness
ISSN:1468-1218, 1878-5719
Online Access:Get full text
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Summary:In this paper, a Stokes hemivariational inequality is studied for incompressible fluid flows with the damping effect. The hemivariational inequality feature is caused by the presence of a nonsmooth slip boundary condition of friction type. Well-posedness of the Stokes hemivariational inequality is established through the consideration of a minimization problem. Mixed finite element methods are introduced to solve the Stokes hemivariational inequality and error estimates are derived for the mixed finite element solutions. The error estimates are of optimal order for low-order mixed element pairs under suitable solution regularity assumptions. An efficient iterative algorithm is introduced to solve the mixed finite element system. Numerical results are reported on the performance of the proposed algorithm and the numerical convergence orders of the finite element solutions.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2024.104131