TY - JOUR
T1 - A second-order, uniquely solvable, energy stable BDF numerical scheme for the phase field crystal model
AU - Li, Qi
AU - Mei, Liquan
AU - You, Bo
N1 - Publisher Copyright:
© 2018 IMACS
PY - 2018/12
Y1 - 2018/12
N2 - In this paper, we propose a second-order time accurate convex splitting scheme for the phase field crystal model. The temporal discretization is based on the second-order backward differentiation formula (BDF) and a convex splitting of the energy functional. The mass conservation, unconditionally unique solvability, unconditionally energy stability and convergence of the numerical scheme are proved rigorously. Mixed finite element method is employed to obtain the fully discrete scheme due to a sixth-order spatial derivative. Numerical experiments are presented to demonstrate the accuracy, mass conservation, energy stability and effectiveness of the proposed scheme.
AB - In this paper, we propose a second-order time accurate convex splitting scheme for the phase field crystal model. The temporal discretization is based on the second-order backward differentiation formula (BDF) and a convex splitting of the energy functional. The mass conservation, unconditionally unique solvability, unconditionally energy stability and convergence of the numerical scheme are proved rigorously. Mixed finite element method is employed to obtain the fully discrete scheme due to a sixth-order spatial derivative. Numerical experiments are presented to demonstrate the accuracy, mass conservation, energy stability and effectiveness of the proposed scheme.
KW - Convex splitting
KW - Energy stability
KW - Finite element method
KW - Phase field crystal model
KW - Second-order accuracy
UR - https://www.scopus.com/pages/publications/85049979672
U2 - 10.1016/j.apnum.2018.07.003
DO - 10.1016/j.apnum.2018.07.003
M3 - 文章
AN - SCOPUS:85049979672
SN - 0168-9274
VL - 134
SP - 46
EP - 65
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -