Error Estimation Of A Class Stable Spectral Approximation Expitaxial Growth Models

Numerical methods for solving the continuum model of the dynamics of the molecular-beam epitaxy require very large time simulation, and therefore large time steps become necessary. In this work, the initial-boundary value problem of two-dimensional molecular-beam epitaxy growth equation is considered. A class of full discrete dissipative Fourier spectral schemes are proposed. The Sobolev imbedding Wp1,1(?) C(Ω) is quoted for the functions with periodic boundary conditions. In particular, there holds Hp1(?)L∞(Ω). The existence of the numerical solution is proved by a series of a priori estimations and the Brower fixed point theorem. The uniqueness of the numerical solution is also discussed. The optimal converge rate is obtained by the energy method. The numerical simulations are performed to demonstrate the effectiveness of the proposed schemes.