TY - JOUR
T1 - An unconditionally energy-stable second-order time-accurate scheme for the Cahn–Hilliard equation on surfaces
AU - Li, Yibao
AU - Kim, Junseok
AU - Wang, Nan
N1 - 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.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - 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.
AB - 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.
KW - Cahn–Hilliard equation
KW - Laplace–Beltrami operator
KW - Mass conservation
KW - Triangular surface mesh
KW - Unconditionally energy-stable
UR - http://www.scopus.com/inward/record.url?scp=85018874090&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2017.05.006
DO - 10.1016/j.cnsns.2017.05.006
M3 - Article
AN - SCOPUS:85018874090
SN - 1007-5704
VL - 53
SP - 213
EP - 227
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
ER -