An unconditionally energy-stable second-order time-accurate scheme for the Cahn–Hilliard equation on surfaces

Yibao Li, Junseok Kim, Nan Wang

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)

Abstract

In this paper, we propose an unconditionally energy-stable second-order time-accurate scheme for the Cahn–Hilliard equation on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. The proposed scheme, which combines a Crank–Nicolson-type scheme with a linearly stabilized splitting scheme, is second-order accurate in time. The discrete system is shown to be conservative and unconditionally energy-stable. The resulting system of discrete equations is simple to implement, and can be solved using a biconjugate gradient stabilized method. We demonstrate the performance of our proposed algorithm through several numerical experiments.

Original languageEnglish
Pages (from-to)213-227
Number of pages15
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume53
DOIs
Publication statusPublished - 2017 Dec 1

Bibliographical note

Funding Information:
This work was funded by Natural Science Basic Research Plan in Shaanxi Province of China(2016JQ1024), by National Natural Science Foundation of China(No. 11601416). The corresponding author (J.S. Kim) was supported by Korea University Future Research Grant. The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have improved the quality of this paper.

Publisher Copyright:
© 2017 Elsevier B.V.

Keywords

  • Cahn–Hilliard equation
  • Laplace–Beltrami operator
  • Mass conservation
  • Triangular surface mesh
  • Unconditionally energy-stable

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

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