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

Mouhamadou Samsidy Goudiaby; Ben Mansour Dia

doi:10.1016/j.rinam.2021.100213

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

Mouhamadou Samsidy Goudiaby^*
, Ben Mansour Dia

^*Corresponding author for this work

Center for Integrative Petroleum Research

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Article number	100213
Journal	Results in Applied Mathematics
Volume	12
DOIs	https://doi.org/10.1016/j.rinam.2021.100213
State	Published - Nov 2021

Bibliographical note

Publisher Copyright:
© 2021 The Author(s)

Keywords

Discrete attractor
Longtime stability
Semi-implicit scheme
Two-phase flow

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.rinam.2021.100213

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title = "Longtime behavior of a semi-implicit scheme for Caginalp phase-field model",

abstract = "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.",

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N2 - 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.

AB - 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.

KW - Discrete attractor

KW - Longtime stability

KW - Semi-implicit scheme

KW - Two-phase flow

UR - https://www.scopus.com/pages/publications/85118881446

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DO - 10.1016/j.rinam.2021.100213

M3 - Article

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JO - Results in Applied Mathematics

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ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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