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 splitti...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.展开更多
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)+1 种基金supported in part by NSFC Grant(No.12071496)Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(No.2020B1212060032)。
文摘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.
