关于薄膜外延生长模型隐式全离散格式的误差分析  

CONVERGENCE ANALYSIS OF IMPLICIT FULL DISCRETIZATION FOR THE EPITAXIAL GROWTH MODEL OF THIN FILMS

作　　者：夏茜[1] 陈文斌[1] 刘建国[2] 

机构地区：[1]复旦大学数学科学学院,上海200433 [2]美国MD马里兰大学数学系,207424015

出　　处：《高等学校计算数学学报》2012年第1期30-51,共22页Numerical Mathematics A Journal of Chinese Universities

基　　金：973高性能科学计算研究(G2005CB321701);国家自然科学基金(10431030;10771138);上海市自然科学基金(07JC14001)

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。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.

关 键 词：全离散格式 误差分析 生长模型 薄膜外延 非线性扩散方程 隐式 增长模型 分子薄膜 

分 类 号：O241.82[理学—计算数学]