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

被引：0
|
作者：
El Moutea, Omar [1 ]
Nakbi, Nadia [2 ]
El Akkad, Abdeslam [2 ,3 ]
Elkhalfi, Ahmed [3 ]
El Ouadefli, Lahcen [3 ]
Vlase, Sorin [4 ,5 ]
Scutaru, Maria Luminita [4 ]
机构：
[1] Hassan II Univ, ENS, Lab Math & Applicat, Casablanca 20000, Morocco
[2] Ctr Reg Metiers Educ & Format Fes Meknes CRMEF Fes, Dept Math, Rue Koweit 49, Fes 30050, Morocco
[3] Univ Sidi Mohammed Ben Abdellah, Fac Sci & Technol, Mech Engn Lab, Route Imouzzer, Fes 30000, Morocco
[4] Transylvania Univ Brasov, Fac Mech Engn, Dept Mech Engn, B Dul Eroilor 29, Brasov 500036, Romania
[5] Romanian Acad Tech Sci, B Dul Dacia 26, Bucharest 030167, Romania
来源：
SYMMETRY-BASEL | 2023年 / 15卷 / 11期
关键词：
a posteriori error indicators; general boundary condition; finite element method (FEM); unsteady incompressible Navier-Stokes equations; IFISS software; COMSOL multiphysics; ADINA system; POSTERIORI ERROR ESTIMATION; SOLVER; GMRES;
D O I：
10.3390/sym15112031
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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.
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页数：24
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