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A Posteriori Error Estimators for the Quasi-Newtonian Stokes Problem with a General Boundary Condition

Author

Listed:
  • Omar El Moutea

    (Laboratory of Mathematics and Applications, ENS, Hassan II University Casablanca, Casablanca 20000, Morocco)

  • Lahcen El Ouadefli

    (Mechanical Engineering Laboratory, Faculty of Science and Technology, University Sidi Mohammed Ben Abdellah, B.P. 30000 Route Imouzzer, Fez 30000, Morocco)

  • Abdeslam El Akkad

    (Mechanical Engineering Laboratory, Faculty of Science and Technology, University Sidi Mohammed Ben Abdellah, B.P. 30000 Route Imouzzer, Fez 30000, Morocco
    Département de Mathématiques, Centre Regional des Métiers d’Education et de Formation de Fès Meknès (CRMEF Fès-Meknès), Rue de Koweit 49, Ville Nouvelle, Fez 30050, Morocco)

  • Nadia Nakbi

    (Département de Mathématiques, Centre Regional des Métiers d’Education et de Formation de Fès Meknès (CRMEF Fès-Meknès), Rue de Koweit 49, Ville Nouvelle, Fez 30050, Morocco)

  • Ahmed Elkhalfi

    (Mechanical Engineering Laboratory, Faculty of Science and Technology, University Sidi Mohammed Ben Abdellah, B.P. 30000 Route Imouzzer, Fez 30000, Morocco)

  • Maria Luminita Scutaru

    (Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transylvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania)

  • Sorin Vlase

    (Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transylvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania
    Romanian Academy of Technical Sciences, B-dul Dacia 26, 030167 Bucharest, Romania)

Abstract

In this paper, we approach two nonlinear differential equations applied in fluid mechanics by finite element methods (FEM). Our objective is to approach the solution to these problems; the first one is the “ p -Laplacian” problem and the second one is the “Quasi-Newtonian Stokes” problem with a general boundary condition. To study and analyze our solutions, we introduce the a posteriori error indicator; this technique allows us to control the error, and each is shown the equivalent between the true and the a posterior errors estimators. The performance of the finite element method by this type of general boundary condition is presented via different numerical simulations.

Suggested Citation

  • Omar El Moutea & Lahcen El Ouadefli & Abdeslam El Akkad & Nadia Nakbi & Ahmed Elkhalfi & Maria Luminita Scutaru & Sorin Vlase, 2023. "A Posteriori Error Estimators for the Quasi-Newtonian Stokes Problem with a General Boundary Condition," Mathematics, MDPI, vol. 11(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1943-:d:1128571
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    References listed on IDEAS

    as
    1. Lahcen El Ouadefli & Abdeslam El Akkad & Omar El Moutea & Hassan Moustabchir & Ahmed Elkhalfi & Maria Luminița Scutaru & Radu Muntean, 2022. "Numerical Simulation for Brinkman System with Varied Permeability Tensor," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
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    Cited by:

    1. Maria Luminița Scutaru & Sohaib Guendaoui & Ouadie Koubaiti & Lahcen El Ouadefli & Abdeslam El Akkad & Ahmed Elkhalfi & Sorin Vlase, 2023. "Flow of Newtonian Incompressible Fluids in Square Media: Isogeometric vs. Standard Finite Element Method," Mathematics, MDPI, vol. 11(17), pages 1-14, August.

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    1. Maria Luminița Scutaru & Sohaib Guendaoui & Ouadie Koubaiti & Lahcen El Ouadefli & Abdeslam El Akkad & Ahmed Elkhalfi & Sorin Vlase, 2023. "Flow of Newtonian Incompressible Fluids in Square Media: Isogeometric vs. Standard Finite Element Method," Mathematics, MDPI, vol. 11(17), pages 1-14, August.

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