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Error estimates for time discretizations of Cahn–Hilliard and Allen–Cahn phase-field models for two-phase incompressible flows

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Abstract

We carry out rigorous error analysis for some energy stable time discretization schemes developed in Shen and Yang (SIAM J Sci Comput 32(3):1159–1179, 2010) for a Cahn–Hilliard phase-field model and in Shen and Yang (Chin Ann Math Ser B 31(5):743–758, 2010) for an Allen–Cahn phase-field model.

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Authors and Affiliations

  1. Beijing Computational Science Research Center, Beijing, 100193, China

    Yongyong Cai

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-1957, USA

    Yongyong Cai, Heejun Choi & Jie Shen

Authors
  1. Yongyong Cai
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  2. Heejun Choi
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  3. Jie Shen
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Corresponding author

Correspondence to Jie Shen.

Additional information

This work is partially supported by NSF Grants DMS-1419053, DMS-1620262 and AFOSR FA9550-16-1-0102, and by NSFC U1530401 and NSFC 91630204.

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Cai, Y., Choi, H. & Shen, J. Error estimates for time discretizations of Cahn–Hilliard and Allen–Cahn phase-field models for two-phase incompressible flows. Numer. Math. 137, 417–449 (2017). https://doi.org/10.1007/s00211-017-0875-9

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  • DOI: https://doi.org/10.1007/s00211-017-0875-9

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