Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in [Formula: see text] with L(2) Initial Data

In this paper, we study the finite element method of the Navier–Stokes equations with the initial data belonging to the [Formula: see text] space for all time [Formula: see text]. Due to the poor smoothness of the initial data, the solution of the problem is singular, although in the [Formula: see t...

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Detalles Bibliográficos
Autores principales: Ren, Shuyan, Wang, Kun, Feng, Xinlong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217603/
https://www.ncbi.nlm.nih.gov/pubmed/37238481
http://dx.doi.org/10.3390/e25050726
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author Ren, Shuyan
Wang, Kun
Feng, Xinlong
author_facet Ren, Shuyan
Wang, Kun
Feng, Xinlong
author_sort Ren, Shuyan
collection PubMed
description In this paper, we study the finite element method of the Navier–Stokes equations with the initial data belonging to the [Formula: see text] space for all time [Formula: see text]. Due to the poor smoothness of the initial data, the solution of the problem is singular, although in the [Formula: see text]-norm, when [Formula: see text]. Under the uniqueness condition, by applying the integral technique and the estimates in the negative norm, we deduce the uniform-in-time optimal error bounds for the velocity in [Formula: see text]-norm and the pressure in [Formula: see text]-norm.
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spelling pubmed-102176032023-05-27 Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in [Formula: see text] with L(2) Initial Data Ren, Shuyan Wang, Kun Feng, Xinlong Entropy (Basel) Article In this paper, we study the finite element method of the Navier–Stokes equations with the initial data belonging to the [Formula: see text] space for all time [Formula: see text]. Due to the poor smoothness of the initial data, the solution of the problem is singular, although in the [Formula: see text]-norm, when [Formula: see text]. Under the uniqueness condition, by applying the integral technique and the estimates in the negative norm, we deduce the uniform-in-time optimal error bounds for the velocity in [Formula: see text]-norm and the pressure in [Formula: see text]-norm. MDPI 2023-04-27 /pmc/articles/PMC10217603/ /pubmed/37238481 http://dx.doi.org/10.3390/e25050726 Text en © 2023 by the authors. 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
Ren, Shuyan
Wang, Kun
Feng, Xinlong
Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in [Formula: see text] with L(2) Initial Data
title Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in [Formula: see text] with L(2) Initial Data
title_full Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in [Formula: see text] with L(2) Initial Data
title_fullStr Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in [Formula: see text] with L(2) Initial Data
title_full_unstemmed Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in [Formula: see text] with L(2) Initial Data
title_short Uniform Error Estimates of the Finite Element Method for the Navier–Stokes Equations in [Formula: see text] with L(2) Initial Data
title_sort uniform error estimates of the finite element method for the navier–stokes equations in [formula: see text] with l(2) initial data
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10217603/
https://www.ncbi.nlm.nih.gov/pubmed/37238481
http://dx.doi.org/10.3390/e25050726
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AT wangkun uniformerrorestimatesofthefiniteelementmethodforthenavierstokesequationsinformulaseetextwithl2initialdata
AT fengxinlong uniformerrorestimatesofthefiniteelementmethodforthenavierstokesequationsinformulaseetextwithl2initialdata

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