Stokes and Navier-Stokes equations under power law slip boundary condition: Numerical analysis
In this work, we study theoretically and numerically the equations of Stokes and Navier-Stokes under power law slip boundary condition. We establish existence of a unique solution by using the monotone operators theory for the Stokes equations whereas for the Navier-Stokes equations, we construct th...
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| Vydáno v: | Computers & mathematics with applications (1987) Ročník 128; s. 198 - 213 |
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| Jazyk: | angličtina |
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Elsevier Ltd
15.12.2022
Elsevier |
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| ISSN: | 0898-1221, 1873-7668 |
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| Abstract | In this work, we study theoretically and numerically the equations of Stokes and Navier-Stokes under power law slip boundary condition. We establish existence of a unique solution by using the monotone operators theory for the Stokes equations whereas for the Navier-Stokes equations, we construct the solution by means of Galerkin's approximation combined with some compactness results. Next, we formulate and analyze the finite element approximations associated to these problems. We derive optimal and sub-optimal a priori error estimate for both problems depending how the monotonicity is used. Iterative schemes for solving the nonlinear problems are formulated and convergence is studied. Numerical experiments presented confirm the theoretical findings.
•New power law slip boundary condition for the Stokes and Navier Stokes system.•Well posedness and optimal convergence rates for standard finite element spaces.•Formulation and analysis of the iterative scheme.•Verification of the convergence properties, simulation of the Lid driven cavity. |
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| AbstractList | In this work, we study theoretically and numerically the equations of Stokes and Navier-Stokes under power law slip boundary condition. We establish existence of a unique solution by using the monotone operators theory for the Stokes equations whereas for the Navier-Stokes equations, we construct the solution by means of Galerkin's approximation combined with some compactness results. Next, we formulate and analyze the finite element approximations associated to these problems. We derive optimal and sub-optimal a priori error estimate for both problems depending how the monotonicity is used. Iterative schemes for solving the nonlinear problems are formulated and convergence is studied. Numerical experiments presented confirm the theoretical findings. In this work, we study theoretically and numerically the equations of Stokes and Navier-Stokes under power law slip boundary condition. We establish existence of a unique solution by using the monotone operators theory for the Stokes equations whereas for the Navier-Stokes equations, we construct the solution by means of Galerkin's approximation combined with some compactness results. Next, we formulate and analyze the finite element approximations associated to these problems. We derive optimal and sub-optimal a priori error estimate for both problems depending how the monotonicity is used. Iterative schemes for solving the nonlinear problems are formulated and convergence is studied. Numerical experiments presented confirm the theoretical findings. •New power law slip boundary condition for the Stokes and Navier Stokes system.•Well posedness and optimal convergence rates for standard finite element spaces.•Formulation and analysis of the iterative scheme.•Verification of the convergence properties, simulation of the Lid driven cavity. |
| Author | Sayah, Toni Djoko, J.K. Koko, J. Mbehou, M. |
| Author_xml | – sequence: 1 givenname: J.K. orcidid: 0000-0002-3278-460X surname: Djoko fullname: Djoko, J.K. email: jules.djokokamdem@gmail.com organization: African peer review mechanism, Johannesburg, South Africa – sequence: 2 givenname: J. surname: Koko fullname: Koko, J. email: jonas.koko@uca.fr organization: LIMOS, Université Clermont-Auvergne – CNRS UMR 6158, B.P 10448, 63000 Clermont-Ferrand, France – sequence: 3 givenname: M. orcidid: 0000-0002-3938-0800 surname: Mbehou fullname: Mbehou, M. email: mbehoumoh@gmail.com organization: Departement de Mathematiques, Faculté des Sciences, Université de Yaounde 1, Yaounde, Cameroon – sequence: 4 givenname: Toni surname: Sayah fullname: Sayah, Toni email: toni.sayah@usj.edu.lb organization: Laboratoire de Mathematiques et Applications, Unite de recherche “Mathematiques et Modelisation”, Faculté des Sciences, Université Saint-Joseph, B.P 11-514 Riad El Solh, Beirut 1107 2050, Lebanon |
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| Cites_doi | 10.1007/s40324-014-0012-y 10.1017/S0022112005008025 10.1063/1.4719780 10.1007/BF01385799 10.1016/j.compositesa.2017.04.021 10.1016/j.cma.2016.03.026 10.1615/InterJFluidMechRes.2017015434 10.1515/jnum-2012-0013 10.1142/S0218202598000652 10.1007/s10915-005-4933-6 10.1080/10402004.2015.1068422 10.1007/s00211-014-0646-9 10.1007/978-3-642-36519-5 10.1142/S0218202504003556 10.1016/j.jmaa.2018.05.020 10.1051/m2an/2019008 10.1051/m2an/1993270201311 10.1002/mma.5443 10.1080/10618562.2013.821114 10.1007/BF01398380 10.1016/j.jcp.2005.11.021 10.1016/j.apnum.2006.10.005 10.1016/j.cis.2014.02.015 10.1142/S0218202502001933 10.1007/BF01385609 10.1063/1.4906091 10.1007/s00211-008-0157-7 |
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| Keywords | Finite element method Error estimates Power law slip boundary condition Monotonicity Stokes equations Navier-Stokes equations finite element method rate of convergence monotonicity power law slip boundary condition error estimates |
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| SubjectTerms | Error estimates Finite element method Mathematics Monotonicity Navier-Stokes equations Numerical Analysis Power law slip boundary condition Stokes equations |
| Title | Stokes and Navier-Stokes equations under power law slip boundary condition: Numerical analysis |
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