二维Cahn-Hilliard方程半隐的预估-校正谱逼近(英文)  

Semi-implicit prediction-correction spectral approximation to two-dimensional Cahn-Hilliard equation

作　　者：贺力平[1,2] 

机构地区：[1]上海交通大学数学系,上海200030 [2]上海交通大学教育部科学工程计算重点实验室,上海200234

出　　处：《应用数学与计算数学学报》2013年第1期128-146,共19页Communication on Applied Mathematics and Computation

基　　金：supported by the National Natural Science Foundation of China(11171218;11271258);the Special Foundation of Shanghai Jiao Tong University for Science and Technology Innovation(AE0710004)

摘　　要：针对二维Cahn-Hilliard方程的初边值问题提出了一个便于计算的、半隐的预估-校正谱格式.通过引入两个三线性泛函,克服了非线性项所带来的困难,并用能量方法严格证明了数值解在时间方向具有二阶精度,而在空间方向具有谱精度.The initial-boundary value problem of two-dimensional Cahn-Hilliard equation is considered. A semi-implicit prediction-correction Fourier spectral scheme is presented, which is easy to be performed. Two trilinear functions are introduced to deal with the nonlinear term. It is strictly proved by the energy method that the numerical solution possesses the accuracy of second order in time and higher order in space.

关 键 词：CAHN-HILLIARD方程 半隐式的预估-校正谱格式 高精度 收敛性 

分 类 号：O175.8[理学—数学]