Longtime behavior of a semi-implicit scheme for Caginalp phase-field model

We present a semi-implicit scheme for the Caginalp phase-field model. The scheme is a combination of implicit Euler scheme together with Eyre’s decomposition. We prove the uniqueness of the numerical solution for small time-step and the unconditional stability of the scheme. We also show that the gl...

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Autores principales:	Mouhamadou Samsidy Goudiaby, Ben Mansour Dia
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Semi-implicit scheme Longtime stability Discrete attractor Two-phase flow Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8bfeaead75514e1d885bbaca68286623
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spelling	oai:doaj.org-article:8bfeaead75514e1d885bbaca682866232021-11-10T04:40:27ZLongtime behavior of a semi-implicit scheme for Caginalp phase-field model2590-037410.1016/j.rinam.2021.100213https://doaj.org/article/8bfeaead75514e1d885bbaca682866232021-11-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2590037421000492https://doaj.org/toc/2590-0374We present a semi-implicit scheme for the Caginalp phase-field model. The scheme is a combination of implicit Euler scheme together with Eyre’s decomposition. We prove the uniqueness of the numerical solution for small time-step and the unconditional stability of the scheme. We also show that the global attractors generated by the scheme converges to the global attractor of the continuous problem as the time step goes to zero.Mouhamadou Samsidy GoudiabyBen Mansour DiaElsevierarticleSemi-implicit schemeLongtime stabilityDiscrete attractorTwo-phase flowMathematicsQA1-939ENResults in Applied Mathematics, Vol 12, Iss , Pp 100213- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Semi-implicit scheme Longtime stability Discrete attractor Two-phase flow Mathematics QA1-939
spellingShingle	Semi-implicit scheme Longtime stability Discrete attractor Two-phase flow Mathematics QA1-939 Mouhamadou Samsidy Goudiaby Ben Mansour Dia Longtime behavior of a semi-implicit scheme for Caginalp phase-field model
description	We present a semi-implicit scheme for the Caginalp phase-field model. The scheme is a combination of implicit Euler scheme together with Eyre’s decomposition. We prove the uniqueness of the numerical solution for small time-step and the unconditional stability of the scheme. We also show that the global attractors generated by the scheme converges to the global attractor of the continuous problem as the time step goes to zero.
format	article
author	Mouhamadou Samsidy Goudiaby Ben Mansour Dia
author_facet	Mouhamadou Samsidy Goudiaby Ben Mansour Dia
author_sort	Mouhamadou Samsidy Goudiaby
title	Longtime behavior of a semi-implicit scheme for Caginalp phase-field model
title_short	Longtime behavior of a semi-implicit scheme for Caginalp phase-field model
title_full	Longtime behavior of a semi-implicit scheme for Caginalp phase-field model
title_fullStr	Longtime behavior of a semi-implicit scheme for Caginalp phase-field model
title_full_unstemmed	Longtime behavior of a semi-implicit scheme for Caginalp phase-field model
title_sort	longtime behavior of a semi-implicit scheme for caginalp phase-field model
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/8bfeaead75514e1d885bbaca68286623
work_keys_str_mv	AT mouhamadousamsidygoudiaby longtimebehaviorofasemiimplicitschemeforcaginalpphasefieldmodel AT benmansourdia longtimebehaviorofasemiimplicitschemeforcaginalpphasefieldmodel
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Longtime behavior of a semi-implicit scheme for Caginalp phase-field model

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