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Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations †
In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair [Formula: see text]. The method consists of transmitting the finite element solution [Formula: see text] of the 3D steady Navier–Stokes equations into the finite element...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2021
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8699973/ https://www.ncbi.nlm.nih.gov/pubmed/34945965 http://dx.doi.org/10.3390/e23121659 |
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author | He, Yinnian |
author_facet | He, Yinnian |
author_sort | He, Yinnian |
collection | PubMed |
description | In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair [Formula: see text]. The method consists of transmitting the finite element solution [Formula: see text] of the 3D steady Navier–Stokes equations into the finite element solution pairs [Formula: see text] based on the finite element space pair [Formula: see text] of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair [Formula: see text] satisfies the discrete inf-sup condition in a 3D domain [Formula: see text]. Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution [Formula: see text] of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to [Formula: see text] of the FE solution [Formula: see text] to the exact solution [Formula: see text] of the 3D steady Navier–Stokes equations in the [Formula: see text] norm. Finally, we also give the convergence order with respect to [Formula: see text] of the FE velocity [Formula: see text] to the exact velocity u of the 3D steady Navier–Stokes equations in the [Formula: see text] norm. |
format | Online Article Text |
id | pubmed-8699973 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-86999732021-12-24 Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations † He, Yinnian Entropy (Basel) Article In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair [Formula: see text]. The method consists of transmitting the finite element solution [Formula: see text] of the 3D steady Navier–Stokes equations into the finite element solution pairs [Formula: see text] based on the finite element space pair [Formula: see text] of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair [Formula: see text] satisfies the discrete inf-sup condition in a 3D domain [Formula: see text]. Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution [Formula: see text] of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to [Formula: see text] of the FE solution [Formula: see text] to the exact solution [Formula: see text] of the 3D steady Navier–Stokes equations in the [Formula: see text] norm. Finally, we also give the convergence order with respect to [Formula: see text] of the FE velocity [Formula: see text] to the exact velocity u of the 3D steady Navier–Stokes equations in the [Formula: see text] norm. MDPI 2021-12-09 /pmc/articles/PMC8699973/ /pubmed/34945965 http://dx.doi.org/10.3390/e23121659 Text en © 2021 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article He, Yinnian Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations † |
title | Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations † |
title_full | Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations † |
title_fullStr | Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations † |
title_full_unstemmed | Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations † |
title_short | Finite Element Iterative Methods for the 3D Steady Navier–Stokes Equations † |
title_sort | finite element iterative methods for the 3d steady navier–stokes equations † |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8699973/ https://www.ncbi.nlm.nih.gov/pubmed/34945965 http://dx.doi.org/10.3390/e23121659 |
work_keys_str_mv | AT heyinnian finiteelementiterativemethodsforthe3dsteadynavierstokesequations |