中文摘要：

分子薄膜的外延增长模型是由四阶非线性扩散方程描述的：设区域Ω=[0，L]2，外延表面高度函数h（x，t）满足如下方程

英文摘要：

In this paper, the implicit full discreticzation for the epitaxial growth mode of thin films is analyzed. A modified partial differential equation is intro- duced to approximate the original epitaxial growth model, and the wellpossness of the modified equation is obtained by Faedo-Galerkin method. The convergences and errors of the spectral Galerkin method in the spatial discretization and back- ward Euler method in the time discreetization are obtained.