@Article{AAMM-16-1,
author = {Xu, Minqiang and Zou, Qingsong},
title = {A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2024},
volume = {16},
number = {1},
pages = {1--23},
abstract = {<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>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0193},
url = {https://global-sci.com/article/72798/a-hessian-recovery-based-linear-finite-element-method-for-molecular-beam-epitaxy-growth-model-with-slope-selection}
}