An Efficient and Unconditionally Energy Stable Fully Discrete Scheme for the Confined Ternary Blended Polymers Model (CSIAM Transactions on Applied Mathematics, 2022)
In this paper, we develop a fully discrete scheme to solve the confinedternary blended polymers (TBP) model with four order parameters based on thestabilized-scalar auxiliary variable (S-SAV) approach in time and the Fourier spectralmethod 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 discretescheme converges with order $\mathcal{O}(τ^2+h^m)$ in the sense of the $L^2$ norm, where $τ$ is thetime 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 Januscore-shell particles, is presented to show the morphological structures.
Keywords: Confinement; ternary blended polymers; unconditional energy stability; error estimates; Fourier spectral method.