TY - JOUR
T1 - A Novel Second-Order Scheme for the Molecular Beam Epitaxy Model with Slope Selection
AU - Lizhen Chen, Jia Zhao & Yuezheng Gong
JO - Communications in Computational Physics
VL - 4
SP - 1024
EP - 1044
PY - 2018
DA - 2018/12
SN - 25
DO - http://doi.org/10.4208/cicp.OA-2018-0015
UR - https://global-sci.org/intro/article_detail/cicp/12889.html
KW - Phase field, linear scheme, molecular beam epitaxy, energy stable.
AB - <p style="text-align: justify;">Molecular beam epitaxy (MBE) is an important and challenging research
topic in material science. In this paper, we propose a new fully discrete scheme for
the well-celebrated continuum MBE model with slope selection. First of all, we use a
multi-step strategy to discretize the MBE model in time. The obtained semi-discrete
scheme is proved to possess properties of total mass conservation, unconditionally energy stability and uniquely solvability. The rigorous error estimate is then conducted
to show its second-order convergence. The semi-discrete scheme is further discretized
in space using the Fourier pseudo-spectral method. The fully discrete scheme is also
shown to preserve mass-conservation and energy-dissipation properties. Afterward,
several numerical examples are presented to validate the accuracy and efficiency of
our proposed scheme. In particular, the scaling law for the roughness growing and
effective energy decaying are captured during long-time coarsening dynamic simulations. The idea proposed in this paper could be readily utilized to design accurate and
stable numerical approximations for many other energy-based phase field models.</p>