L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation

In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numeric...

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Detalles Bibliográficos
Autor principal: Wang, Zhen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Nature Singapore 2023
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10088693/
https://www.ncbi.nlm.nih.gov/pubmed/37360904
http://dx.doi.org/10.1007/s42967-023-00257-x
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author Wang, Zhen
author_facet Wang, Zhen
author_sort Wang, Zhen
collection PubMed
description In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be [Formula: see text] -robust using the newly established Gronwall inequalities, that is, it remains valid when [Formula: see text] . Numerical experiments are given to demonstrate the theoretical statements.
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spelling pubmed-100886932023-04-12 L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation Wang, Zhen Commun Appl Math Comput Original Paper In this paper, a class of discrete Gronwall inequalities is proposed. It is efficiently applied to analyzing the constructed L1/local discontinuous Galerkin (LDG) finite element methods which are used for numerically solving the Caputo-Hadamard time fractional diffusion equation. The derived numerical methods are shown to be [Formula: see text] -robust using the newly established Gronwall inequalities, that is, it remains valid when [Formula: see text] . Numerical experiments are given to demonstrate the theoretical statements. Springer Nature Singapore 2023-04-11 /pmc/articles/PMC10088693/ /pubmed/37360904 http://dx.doi.org/10.1007/s42967-023-00257-x Text en © Shanghai University 2023, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Original Paper
Wang, Zhen
L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation
title L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation
title_full L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation
title_fullStr L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation
title_full_unstemmed L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation
title_short L1/LDG Method for Caputo-Hadamard Time Fractional Diffusion Equation
title_sort l1/ldg method for caputo-hadamard time fractional diffusion equation
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10088693/
https://www.ncbi.nlm.nih.gov/pubmed/37360904
http://dx.doi.org/10.1007/s42967-023-00257-x
work_keys_str_mv AT wangzhen l1ldgmethodforcaputohadamardtimefractionaldiffusionequation

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