A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection  

作　　者：Minqiang Xu Qingsong Zou 

机构地区：[1]College of Science,Zhejiang University of Technology,Hangzhou,Zhejiang 310023,China [2]School of Computer Science and Engineering,Sun Yat-Sen University,Guangzhou,Guangdong 510275,China [3]School of Computer Science and Engineering,and Guangdong Province Key Laboratory of Computational Science,Sun Yat-Sen University,Guangzhou,Guangdong 510275,China

出　　处：《Advances in Applied Mathematics and Mechanics》2024年第1期1-23,共23页应用数学与力学进展（英文）

基　　金：supported by General Scientific Research Projects of Zhejiang Education Department(No.Y202147013);the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-Sen University(No.2021008);supported in part by NSFC Grant(No.12071496);Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(No.2020B1212060032)。

摘　　要：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 secondorder 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.

关 键 词：Molecular beam epitaxy Hessian recovery linear finite element method superconvergence. 

分 类 号：O241.82[理学—计算数学]