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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| Published in: | Nonlinear analysis: real world applications Vol. 79; p. 104131 |
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| Format: | Journal Article |
| Language: | English |
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01.10.2024
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| ISSN: | 1468-1218, 1878-5719 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 104131 |
| Author | Qiu, Hailong Mei, Liquan Han, Weimin |
| Author_xml | – sequence: 1 givenname: Weimin surname: Han fullname: Han, Weimin email: weimin-han@uiowa.edu organization: Department of Mathematics, University of Iowa, Iowa City, IA 52242-1410, USA – sequence: 2 givenname: Hailong surname: Qiu fullname: Qiu, Hailong email: hail_qiu@126.com organization: School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, 224051, China – sequence: 3 givenname: Liquan surname: Mei fullname: Mei, Liquan email: lqmei@xjtu.edu.cn organization: School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, China |
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| Cites_doi | 10.1093/imanum/drz032 10.1137/140963248 10.1142/S0218202505000686 10.1007/s00220-003-0859-8 10.1016/j.cma.2016.03.026 10.1016/j.aml.2021.107401 10.1016/j.nonrwa.2020.103114 10.1080/01630563.2021.1881541 10.1007/s10915-018-0644-7 10.1002/fld.2574 10.1007/s10255-011-0063-0 10.1016/j.jmaa.2004.12.033 10.1007/BF02576171 10.1007/s00211-010-0354-z 10.1007/978-1-4614-4232-5 10.1090/S0002-9947-02-03034-9 10.1016/j.nonrwa.2016.02.005 10.1002/mma.802 10.1016/j.amc.2008.06.035 10.1017/S0962492919000023 10.1016/j.camwa.2019.04.024 10.1007/s10915-021-01614-9 10.3846/1392-6292.2007.12.483-495 10.1016/S0022-247X(03)00009-X 10.1007/s13160-012-0098-5 10.1137/120896396 10.1081/PDE-120020499 |
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| Keywords | Hemivariational inequality Mixed finite element method Error estimation Minimization principle Stokes equations with damping Well-posedness |
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| Snippet | In this paper, a Stokes hemivariational inequality is studied for incompressible fluid flows with the damping effect. The hemivariational inequality feature is... |
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| SubjectTerms | Error estimation Hemivariational inequality Minimization principle Mixed finite element method Stokes equations with damping Well-posedness |
| Title | On a Stokes hemivariational inequality for incompressible fluid flows with damping |
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