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

Omar El Moutea, Lahcen El Ouadefli, Abdeslam El Akkad, Nadia Nakbi, Ahmed Elkhalfi, Maria Luminita Scutaru () and Sorin Vlase
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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
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

Mathematics, 2023, vol. 11, issue 8, 1-20

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.

Keywords: a posteriori error estimation; FEM; Laplacian operator; quasi-Newtonian flows problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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