A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection
Year: 2024
Author: Minqiang Xu, Qingsong Zou
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 1–23
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0193
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 1 : pp. 1–23
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Molecular beam epitaxy Hessian recovery linear finite element method superconvergence.
Author Details
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