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Error estimates for a fully discretized scheme to a Cahn-Hilliard phase-field model for two-phase incompressible flows


Authors: Yongyong Cai and Jie Shen
Journal: Math. Comp. 87 (2018), 2057-2090
MSC (2010): Primary 35Q30, 65M12, 65M60
DOI: https://doi.org/10.1090/mcom/3280
Published electronically: November 28, 2017
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Abstract: In this paper, we carry out a rigorous error analysis for a finite-element discretization of the linear, weakly coupled energy stable scheme introduced by Shen and Yang for a Cahn-Hilliard phase-field model of two-phase incompressible flows with matching density.


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Additional Information

Yongyong Cai
Affiliation: Beijing Computational Science Research Center, Beijing, 100193
Email: yongyong.cai@csrc.ac.cn

Jie Shen
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1957—and—School of Mathematical Sciences, Xiamen University, Xiamen, 360115, P.R. China
Email: shen7@purdue.edu

DOI: https://doi.org/10.1090/mcom/3280
Keywords: Phase-field model, Cahn-Hilliard equation, Navier-Stokes equation, finite element, error estimates.
Received by editor(s): December 2, 2015
Received by editor(s) in revised form: September 21, 2016, and March 23, 2017
Published electronically: November 28, 2017
Additional Notes: This work was partially supported by NSF grants DMS-1419053, DMS-1620262 and AFOSR grant FA9550-16-1-0102 and by NSFC grants 11371298, 11421110001, 91630204, 51661135011.
Article copyright: © Copyright 2017 American Mathematical Society

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