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Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations

Several two-level iterative methods based on nonconforming finite element methods are applied for solving numerically the 2D/3D stationary incompressible MHD equations under different uniqueness conditions. These two-level algorithms are motivated by applying the m iterations on a coarse grid and co...

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Detalles Bibliográficos
Autores principales: Su, Haiyan, Xu, Jiali, Feng, Xinlong
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9141767/
https://www.ncbi.nlm.nih.gov/pubmed/35626472
http://dx.doi.org/10.3390/e24050587
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author Su, Haiyan
Xu, Jiali
Feng, Xinlong
author_facet Su, Haiyan
Xu, Jiali
Feng, Xinlong
author_sort Su, Haiyan
collection PubMed
description Several two-level iterative methods based on nonconforming finite element methods are applied for solving numerically the 2D/3D stationary incompressible MHD equations under different uniqueness conditions. These two-level algorithms are motivated by applying the m iterations on a coarse grid and correction once on a fine grid. A one-level Oseen iterative method on a fine mesh is further studied under a weak uniqueness condition. Moreover, the stability and error estimate are rigorously carried out, which prove that the proposed methods are stable and effective. Finally, some numerical examples corroborate the effectiveness of our theoretical analysis and the proposed methods.
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spelling pubmed-91417672022-05-28 Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations Su, Haiyan Xu, Jiali Feng, Xinlong Entropy (Basel) Article Several two-level iterative methods based on nonconforming finite element methods are applied for solving numerically the 2D/3D stationary incompressible MHD equations under different uniqueness conditions. These two-level algorithms are motivated by applying the m iterations on a coarse grid and correction once on a fine grid. A one-level Oseen iterative method on a fine mesh is further studied under a weak uniqueness condition. Moreover, the stability and error estimate are rigorously carried out, which prove that the proposed methods are stable and effective. Finally, some numerical examples corroborate the effectiveness of our theoretical analysis and the proposed methods. MDPI 2022-04-22 /pmc/articles/PMC9141767/ /pubmed/35626472 http://dx.doi.org/10.3390/e24050587 Text en © 2022 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
Su, Haiyan
Xu, Jiali
Feng, Xinlong
Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations
title Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations
title_full Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations
title_fullStr Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations
title_full_unstemmed Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations
title_short Optimal Convergence Analysis of Two-Level Nonconforming Finite Element Iterative Methods for 2D/3D MHD Equations
title_sort optimal convergence analysis of two-level nonconforming finite element iterative methods for 2d/3d mhd equations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9141767/
https://www.ncbi.nlm.nih.gov/pubmed/35626472
http://dx.doi.org/10.3390/e24050587
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