TY - JOUR
T1 - A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection
AU - Xu , Minqiang
AU - Zou , Qingsong
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 1
EP - 23
PY - 2023
DA - 2023/12
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2021-0193
UR - https://global-sci.org/intro/article_detail/aamm/22287.html
KW - Molecular beam epitaxy, Hessian recovery, linear finite element method, superconvergence.
AB - <p style="text-align: justify;">In this paper, we present a Hessian recovery based linear finite element
method to simulate the molecular beam epitaxy growth model with slope selection.
For the time discretization, we apply a first-order convex splitting method and second-order Crank-Nicolson scheme. For the space discretization, we utilize the Hessian
recovery operator to approximate second-order derivatives of a $C^0$ linear finite element function and hence the weak formulation of the fourth-order differential operator can be discretized in the linear finite element space. The energy-decay property
of our proposed fully discrete schemes is rigorously proved. The robustness and the
optimal-order convergence of the proposed algorithm are numerically verified. In a
large spatial domain for a long period, we simulate coarsening dynamics, where 1/3-power-law is observed.</p>