A Mixed Finite Element Approximation for Time-Dependent Navier–Stokes Equations with a General Boundary Condition
Omar El Moutea,
Nadia Nakbi,
Abdeslam El Akkad,
Ahmed Elkhalfi,
Lahcen El Ouadefli,
Sorin Vlase,
Maria Luminita Scutaru
Affiliations
Omar El Moutea
Laboratory of Mathematics and Applications-ENS, Hassan II University, Casablanca 20000, 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
Abdeslam El Akkad
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, Route Imouzzer, Fez 30000, Morocco
Lahcen El Ouadefli
Mechanical Engineering Laboratory, Faculty of Science and Technology, University Sidi Mohammed Ben Abdellah, Route Imouzzer, Fez 30000, Morocco
Sorin Vlase
Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transylvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania
Maria Luminita Scutaru
Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transylvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania
In this paper, we present a numerical scheme for addressing the unsteady asymmetric flows governed by the incompressible Navier–Stokes equations under a general boundary condition. We utilized the Finite Element Method (FEM) for spatial discretization and the fully implicit Euler scheme for time discretization. In addition to the theoretical analysis of the error in our numerical scheme, we introduced two types of a posteriori error indicators: one for time discretization and another for spatial discretization, aimed at effectively controlling the error. We established the equivalence between these estimators and the actual error. Furthermore, we conducted numerical simulations in two dimensions to assess the accuracy and effectiveness of our scheme.
