A Mixed Finite Element Approximation for Time-Dependent Navier–Stokes Equations with a General Boundary Condition-Reference-Cited by-同舟云学术

A Mixed Finite Element Approximation for Time-Dependent Navier–Stokes Equations with a General Boundary Condition

Published:2023-11-08 Issue:11 Volume:15 Page:2031
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

El Moutea Omar¹^ORCID,Nakbi Nadia²,El Akkad Abdeslam²³,Elkhalfi Ahmed³^ORCID,El Ouadefli Lahcen³^ORCID,Vlase Sorin⁴⁵^ORCID,Scutaru Maria Luminita⁴

Affiliation:

1. Laboratory of Mathematics and Applications-ENS, Hassan II University, Casablanca 20000, Morocco

2. 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

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

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

5. Romanian Academy of Technical Sciences, B-dul Dacia 26, 030167 Bucharest, Romania

Abstract

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.

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/11/2031/pdf

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