A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations

A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the sim...

Descripción completa

Detalles Bibliográficos
Autores principales: Liu, Yang, Li, Hong, Gao, Wei, He, Siriguleng, Fang, Zhichao
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3967637/
https://www.ncbi.nlm.nih.gov/pubmed/24737957
http://dx.doi.org/10.1155/2014/141467
_version_ 1782309045569323008
author Liu, Yang
Li, Hong
Gao, Wei
He, Siriguleng
Fang, Zhichao
author_facet Liu, Yang
Li, Hong
Gao, Wei
He, Siriguleng
Fang, Zhichao
author_sort Liu, Yang
collection PubMed
description A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L (2)-norm for the scalar unknown u and in (L (2))(2)-norm for its gradient σ. Moreover, we also discuss a priori error estimates in H (1)-norm for the scalar unknown u.
format Online
Article
Text
id pubmed-3967637
institution National Center for Biotechnology Information
language English
publishDate 2014
publisher Hindawi Publishing Corporation
record_format MEDLINE/PubMed
spelling pubmed-39676372014-04-15 A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations Liu, Yang Li, Hong Gao, Wei He, Siriguleng Fang, Zhichao ScientificWorldJournal Research Article A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L (2)-norm for the scalar unknown u and in (L (2))(2)-norm for its gradient σ. Moreover, we also discuss a priori error estimates in H (1)-norm for the scalar unknown u. Hindawi Publishing Corporation 2014-03-09 /pmc/articles/PMC3967637/ /pubmed/24737957 http://dx.doi.org/10.1155/2014/141467 Text en Copyright © 2014 Yang Liu et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Liu, Yang
Li, Hong
Gao, Wei
He, Siriguleng
Fang, Zhichao
A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations
title A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations
title_full A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations
title_fullStr A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations
title_full_unstemmed A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations
title_short A New Mixed Element Method for a Class of Time-Fractional Partial Differential Equations
title_sort new mixed element method for a class of time-fractional partial differential equations
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3967637/
https://www.ncbi.nlm.nih.gov/pubmed/24737957
http://dx.doi.org/10.1155/2014/141467
work_keys_str_mv AT liuyang anewmixedelementmethodforaclassoftimefractionalpartialdifferentialequations
AT lihong anewmixedelementmethodforaclassoftimefractionalpartialdifferentialequations
AT gaowei anewmixedelementmethodforaclassoftimefractionalpartialdifferentialequations
AT hesiriguleng anewmixedelementmethodforaclassoftimefractionalpartialdifferentialequations
AT fangzhichao anewmixedelementmethodforaclassoftimefractionalpartialdifferentialequations
AT liuyang newmixedelementmethodforaclassoftimefractionalpartialdifferentialequations
AT lihong newmixedelementmethodforaclassoftimefractionalpartialdifferentialequations
AT gaowei newmixedelementmethodforaclassoftimefractionalpartialdifferentialequations
AT hesiriguleng newmixedelementmethodforaclassoftimefractionalpartialdifferentialequations
AT fangzhichao newmixedelementmethodforaclassoftimefractionalpartialdifferentialequations

Ejemplares similares