Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation

Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Se...
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Autor*in:	Lin He [verfasserIn] Juncheng Lv [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate

Übergeordnetes Werk:	In: Advances in Difference Equations - SpringerOpen, 2006, (2019), 1, Seite 17
Übergeordnetes Werk:	year:2019 ; number:1 ; pages:17

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.1186/s13662-019-2048-x

Katalog-ID:	DOAJ033021708

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520			\|a Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.
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allfields	10.1186/s13662-019-2048-x doi (DE-627)DOAJ033021708 (DE-599)DOAJcd32ef13253d400596b913d4cbe85c9b DE-627 ger DE-627 rakwb eng QA1-939 Lin He verfasserin aut Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis. Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate Mathematics Juncheng Lv verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2019), 1, Seite 17 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2019 number:1 pages:17 https://doi.org/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/article/cd32ef13253d400596b913d4cbe85c9b kostenfrei http://link.springer.com/article/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 17
spelling	10.1186/s13662-019-2048-x doi (DE-627)DOAJ033021708 (DE-599)DOAJcd32ef13253d400596b913d4cbe85c9b DE-627 ger DE-627 rakwb eng QA1-939 Lin He verfasserin aut Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis. Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate Mathematics Juncheng Lv verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2019), 1, Seite 17 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2019 number:1 pages:17 https://doi.org/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/article/cd32ef13253d400596b913d4cbe85c9b kostenfrei http://link.springer.com/article/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 17
allfields_unstemmed	10.1186/s13662-019-2048-x doi (DE-627)DOAJ033021708 (DE-599)DOAJcd32ef13253d400596b913d4cbe85c9b DE-627 ger DE-627 rakwb eng QA1-939 Lin He verfasserin aut Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis. Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate Mathematics Juncheng Lv verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2019), 1, Seite 17 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2019 number:1 pages:17 https://doi.org/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/article/cd32ef13253d400596b913d4cbe85c9b kostenfrei http://link.springer.com/article/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 17
allfieldsGer	10.1186/s13662-019-2048-x doi (DE-627)DOAJ033021708 (DE-599)DOAJcd32ef13253d400596b913d4cbe85c9b DE-627 ger DE-627 rakwb eng QA1-939 Lin He verfasserin aut Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis. Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate Mathematics Juncheng Lv verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2019), 1, Seite 17 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2019 number:1 pages:17 https://doi.org/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/article/cd32ef13253d400596b913d4cbe85c9b kostenfrei http://link.springer.com/article/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 17
allfieldsSound	10.1186/s13662-019-2048-x doi (DE-627)DOAJ033021708 (DE-599)DOAJcd32ef13253d400596b913d4cbe85c9b DE-627 ger DE-627 rakwb eng QA1-939 Lin He verfasserin aut Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis. Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate Mathematics Juncheng Lv verfasserin aut In Advances in Difference Equations SpringerOpen, 2006 (2019), 1, Seite 17 (DE-627)377755699 (DE-600)2132815-8 16871847 nnns year:2019 number:1 pages:17 https://doi.org/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/article/cd32ef13253d400596b913d4cbe85c9b kostenfrei http://link.springer.com/article/10.1186/s13662-019-2048-x kostenfrei https://doaj.org/toc/1687-1847 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2027 GBV_ILN_2055 GBV_ILN_2088 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019 1 17
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source	In Advances in Difference Equations (2019), 1, Seite 17 year:2019 number:1 pages:17
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topic_facet	Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate Mathematics
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container_title	Advances in Difference Equations
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callnumber-first	Q - Science
author	Lin He
spellingShingle	Lin He misc QA1-939 misc Subdiffusion equation misc Weighted and shifted Grünwald formula misc Finite element method misc Superconvergence estimate misc Mathematics Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation
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topic_title	QA1-939 Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation Subdiffusion equation Weighted and shifted Grünwald formula Finite element method Superconvergence estimate
topic	misc QA1-939 misc Subdiffusion equation misc Weighted and shifted Grünwald formula misc Finite element method misc Superconvergence estimate misc Mathematics
topic_unstemmed	misc QA1-939 misc Subdiffusion equation misc Weighted and shifted Grünwald formula misc Finite element method misc Superconvergence estimate misc Mathematics
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title	Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation
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title_full	Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation
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title_sort	efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation
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title_auth	Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation
abstract	Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.
abstractGer	Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.
abstract_unstemmed	Abstract Based on the weighted and shifted Grünwald formula, a fully discrete finite element scheme is derived for the variable coefficient time-fractional subdiffusion equation. Firstly, the unconditional stable and convergent of the fully discrete scheme in L1(H1) $L^{1}(H^{1})$-norm is proved. Secondly, through a new estimate approach, the superclose properties are obtained. The global superconvergence order O(τ2+hm+1) $\mathcal{O}(\tau ^{2}+h^{m+1})$ is deduced with the help of interpolation postprocessing technique. Finally, some numerical results are provided to verify the theoretical analysis.
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title_short	Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation
url	https://doi.org/10.1186/s13662-019-2048-x https://doaj.org/article/cd32ef13253d400596b913d4cbe85c9b http://link.springer.com/article/10.1186/s13662-019-2048-x https://doaj.org/toc/1687-1847
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Efficient finite element numerical solution of the variable coefficient fractional subdiffusion equation

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