TY - JOUR
T1 - An Efficient and Unconditionally Energy Stable Fully Discrete Scheme for the Confined Ternary Blended Polymers Model
AU - Ji , Guanghua
AU - Xu , Zhen
AU - Yang , Yuqi
JO - CSIAM Transactions on Applied Mathematics
VL - 3
SP - 480
EP - 514
PY - 2022
DA - 2022/08
SN - 3
DO - http://doi.org/10.4208/csiam-am.SO-2021-0036
UR - https://global-sci.org/intro/article_detail/csiam-am/20970.html
KW - Confinement, ternary blended polymers, unconditional energy stability, error estimates, Fourier spectral method.
AB - <p style="text-align: justify;">In this paper, we develop a fully discrete scheme to solve the confined
ternary blended polymers (TBP) model with four order parameters based on the
stabilized-scalar auxiliary variable (S-SAV) approach in time and the Fourier spectral
method in space. Then, theoretical analysis is given for the scheme based on the backward differentiation formula. The unconditional energy stability and mass conservation are derived. Rigorous error analysis is carried out to show that the fully discrete
scheme converges with order $\mathcal{O}(\tau^2+h^m)$ in the sense of the $L^2$ norm, where $\tau$ is the
time step, $h$ is the spatial step, and $m$ is the regularity of the exact solution. Finally,
some numerical results are given to demonstrate the theoretical analysis. Moreover,
the phase separation of two kinds of polymer particles, namely, Ashura and Janus
core-shell particles, is presented to show the morphological structures.</p>