Fast algorithm for viscous Cahn-Hilliard equation  

作　　者：Danxia WANG Yaqian LI Xingxing WANG Hongen JIA 

机构地区：[1]College of Mathematics,Taiyuan University of Technology,Taiyuan,030024,China

出　　处：《Frontiers of Mathematics in China》2022年第4期689-713,共25页中国高等学校学术文摘·数学（英文）

基　　金：supported by the Research Project Supported by Shanxi Scholarship Council of China(No.2021-029);the Key Research and Development(R&D)Projects of Shanxi Province(No.201903D121038);the Natural Science Foundation of Shanxi Province(Nos.201801D121016,201901D111123).

摘　　要：The main purpose of this paper is to solve the viscous Cahn-Hilliard equation via a fast algorithm based on the two time-mesh(TT-M)finite element(FE)method to ease the problem caused by strong nonlinearities.The TT-M FE algorithm includes the following main computing steps.First,a nonlinear FE method is applied on a coarse time-meshτ_(c).Here,the FE method is used for spatial discretization and the implicit second-orderθscheme(containing both implicit Crank-Nicolson and second-order backward difference)is used for temporal discretization.Second,based on the chosen initial iterative value,a linearized FE system on time fine mesh is solved,where some useful coarse numerical solutions are found by Lagrange’s interpolation formula.The analysis for both stability and a priori error estimates is made in detail.Numerical examples are given to demonstrate the validity of the proposed algorithm.Our algorithm is compared with the traditional Galerkin FE method and it is evident that our fast algorithm can save computational time.

关 键 词：Fast algorithm two time-mesh(TT-M)finite element(FE)method viscous Cahn-Hilliard equation STABILITY CPU time 

分 类 号：O17[理学—数学]