A Hessian Recovery Based Linear Finite Element Method for Molecular Beam Epitaxy Growth Model with Slope Selection (Advances in Applied Mathematics and Mechanics, 2023)
In this paper, we present a Hessian recovery based linear finite elementmethod 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 Hessianrecovery 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 propertyof our proposed fully discrete schemes is rigorously proved. The robustness and theoptimal-order convergence of the proposed algorithm are numerically verified. In alarge spatial domain for a long period, we simulate coarsening dynamics, where 1/3-power-law is observed.