Journal article
Analysis and finite element solution of a Navier–Stokes hemivariational inequality for incompressible fluid flows with damping
Nonlinear analysis: real world applications, Vol.87, 104439
02/2026
DOI: 10.1016/j.nonrwa.2025.104439
Abstract
This paper provides a well-posedness analysis and a mixed finite element method for a hemivariational inequality of the stationary Navier–Stokes equations with a nonlinear damping term. The Navier–Stokes hemivariational inequality describes a steady incompressible fluid flow subject to a nonsmooth slip boundary condition of friction type. The well-posedness of the Navier–Stokes hemivariational inequality is established by constructing two auxiliary problems and applying Banach fixed point arguments twice. Mixed finite element methods are introduced to solve the problem, and error estimates for the solutions are derived. The error estimates are of optimal order for low-order mixed element pairs under suitable solution regularity assumptions. An efficient iterative algorithm is presented, and numerical results are provided to verify the theoretical analysis.
•The model proposes a new math framework for incompressible fluid flows with damping effects.•Well-posedness is proved using recent methods in hemivariational inequalities.•Optimal order error estimates are derived for low-order mixed finite elements.•A computational algorithm is developed for practical applications.
Details
- Title: Subtitle
- Analysis and finite element solution of a Navier–Stokes hemivariational inequality for incompressible fluid flows with damping
- Creators
- Wensi Wang - Zhejiang UniversityXiaoliang Cheng - Zhejiang UniversityWeimin Han - Department of Mathematics, University of Iowa, Iowa City, IA, 52242-1410, USA
- Resource Type
- Journal article
- Publication Details
- Nonlinear analysis: real world applications, Vol.87, 104439
- DOI
- 10.1016/j.nonrwa.2025.104439
- ISSN
- 1468-1218
- eISSN
- 1878-5719
- Publisher
- Elsevier Ltd
- Grant note
- Simons Foundation Collaboration, USA Grants: 850737
The authors are grateful to the anonymous reviewers for valuable comments leading to an improvement of the paper. The work was partially supported by Simons Foundation Collaboration, USA Grants, No. 850737.
- Language
- English
- Electronic publication date
- 06/26/2025
- Date published
- 02/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9984843603802771
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