TY - JOUR
T1 - A BDF2-SSAV Numerical Scheme with Fourier-Spectral Method for a Droplet Thin Film Coarsening Model
AU - Zhang , Juan
AU - Dong , Lixiu
AU - Zhang , Zhengru
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 777
EP - 804
PY - 2024
DA - 2024/08
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2024-0016
UR - https://global-sci.org/intro/article_detail/nmtma/23374.html
KW - Droplet coarsening model, scalar auxiliary variable, Fourier-spectral method, energy stability, optimal rate convergence analysis.
AB - <p style="text-align: justify;">A linear and second order numerical scheme is proposed and analyzed for
a droplet thin film coarsening model, with a singular Leonard-Jones energy potential involved. This numerical scheme with unconditional energy stability is based on
the backward differentiation formular (BDF) method in time derivation combining
with the stabilized scalar auxiliary variable approach in time and the Fourier spectral method in space. A second order accurate artificial regularization term, in the
form of $S∆(\phi^{n+1}− 2\phi^n + \phi^{n−1}),$ is added in the numerical scheme to make better
stability of the numerical scheme. Moreover, we present the detail proof for unconditional energy stability property of the numerical scheme, without any restriction
for the time step size. In addition, an $\mathcal{O}(∆t^2+h^m)$ rate convergence estimate in the $ℓ^∞(0, T ; ℓ^2)$ norm are derived in details with the help of a priori assumption for the
error at the previous time step. Some numerical simulation results are presented to
demonstrate the efficiency and accuracy of the second-order numerical scheme.</p>