A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method

In this research article, a discontinuous Galerkin method with a weighted parameter θ and a penalty parameter γ is proposed for solving the first order hyperbolic equation. The key aim of this method is to design an error estimation for both a priori and a posteriori error analysis on general finite...

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Detalles Bibliográficos
Autores principales: Hossain, Muhammad Shakhawat, Xiong, Chunguang, Sun, Huafei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10062668/
https://www.ncbi.nlm.nih.gov/pubmed/36996053
http://dx.doi.org/10.1371/journal.pone.0277126
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author Hossain, Muhammad Shakhawat
Xiong, Chunguang
Sun, Huafei
author_facet Hossain, Muhammad Shakhawat
Xiong, Chunguang
Sun, Huafei
author_sort Hossain, Muhammad Shakhawat
collection PubMed
description In this research article, a discontinuous Galerkin method with a weighted parameter θ and a penalty parameter γ is proposed for solving the first order hyperbolic equation. The key aim of this method is to design an error estimation for both a priori and a posteriori error analysis on general finite element meshes. It is also exposed to the reliability and effectiveness of both parameters in the order of convergence of the solutions. For a posteriori error estimation, residual adaptive mesh- refining algorithm is employed. A series of numerical experiments are illustrated that demonstrate the efficiency of the method.
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spelling pubmed-100626682023-03-31 A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method Hossain, Muhammad Shakhawat Xiong, Chunguang Sun, Huafei PLoS One Research Article In this research article, a discontinuous Galerkin method with a weighted parameter θ and a penalty parameter γ is proposed for solving the first order hyperbolic equation. The key aim of this method is to design an error estimation for both a priori and a posteriori error analysis on general finite element meshes. It is also exposed to the reliability and effectiveness of both parameters in the order of convergence of the solutions. For a posteriori error estimation, residual adaptive mesh- refining algorithm is employed. A series of numerical experiments are illustrated that demonstrate the efficiency of the method. Public Library of Science 2023-03-30 /pmc/articles/PMC10062668/ /pubmed/36996053 http://dx.doi.org/10.1371/journal.pone.0277126 Text en © 2023 Hossain et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Hossain, Muhammad Shakhawat
Xiong, Chunguang
Sun, Huafei
A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method
title A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method
title_full A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method
title_fullStr A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method
title_full_unstemmed A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method
title_short A priori and a posteriori error analysis of the first order hyperbolic equation by using DG method
title_sort priori and a posteriori error analysis of the first order hyperbolic equation by using dg method
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10062668/
https://www.ncbi.nlm.nih.gov/pubmed/36996053
http://dx.doi.org/10.1371/journal.pone.0277126
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