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Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems
The element-free Galerkin (EFG) method with penalty for Stokes problems is proposed and analyzed in this work. A priori error estimates of the penalty method, which is used to deal with Dirichlet boundary conditions, are derived to illustrate its validity in a continuous sense. Based on a feasible a...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9407530/ https://www.ncbi.nlm.nih.gov/pubmed/36010736 http://dx.doi.org/10.3390/e24081072 |
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author | Zhang, Tao Li, Xiaolin |
author_facet | Zhang, Tao Li, Xiaolin |
author_sort | Zhang, Tao |
collection | PubMed |
description | The element-free Galerkin (EFG) method with penalty for Stokes problems is proposed and analyzed in this work. A priori error estimates of the penalty method, which is used to deal with Dirichlet boundary conditions, are derived to illustrate its validity in a continuous sense. Based on a feasible assumption, it is proved that there is a unique weak solution in the modified weak form of penalized Stokes problems. Then, the error bounds with the penalty factor for the EFG discretization are derived, which provide a rationale for choosing an efficient penalty factor. Numerical examples are given to confirm the theoretical results. |
format | Online Article Text |
id | pubmed-9407530 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-94075302022-08-26 Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems Zhang, Tao Li, Xiaolin Entropy (Basel) Article The element-free Galerkin (EFG) method with penalty for Stokes problems is proposed and analyzed in this work. A priori error estimates of the penalty method, which is used to deal with Dirichlet boundary conditions, are derived to illustrate its validity in a continuous sense. Based on a feasible assumption, it is proved that there is a unique weak solution in the modified weak form of penalized Stokes problems. Then, the error bounds with the penalty factor for the EFG discretization are derived, which provide a rationale for choosing an efficient penalty factor. Numerical examples are given to confirm the theoretical results. MDPI 2022-08-03 /pmc/articles/PMC9407530/ /pubmed/36010736 http://dx.doi.org/10.3390/e24081072 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 Zhang, Tao Li, Xiaolin Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems |
title | Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems |
title_full | Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems |
title_fullStr | Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems |
title_full_unstemmed | Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems |
title_short | Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems |
title_sort | analysis of the element-free galerkin method with penalty for stokes problems |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9407530/ https://www.ncbi.nlm.nih.gov/pubmed/36010736 http://dx.doi.org/10.3390/e24081072 |
work_keys_str_mv | AT zhangtao analysisoftheelementfreegalerkinmethodwithpenaltyforstokesproblems AT lixiaolin analysisoftheelementfreegalerkinmethodwithpenaltyforstokesproblems |