摘要
采用标量辅助变量(scalar auxiliary variable, SAV)方法结合重心插值配点法求解二维Allen-Cahn方程.在时间方向上分别采用Crank-Nicolson格式、二阶向后差分格式离散,空间方向上采用重心Lagrange插值配点法离散,建立了两种无条件能量稳定SAV格式,并给出了重心插值配点格式的逼近性质.数值实验表明:两种SAV配点格式的时间收敛阶为二阶,并满足能量递减规律.与空间采用有限差分法离散对比,重心Lagrange配点格式具有指数收敛的特性.
The scalar auxiliary variable(SAV)approach combined with the barycentric interpolation colloca⁃tion method was proposed to solve the 2D Allen⁃Cahn equation.Two unconditional energy⁃stable SAV schemes were constructed based on the Crank⁃Nicolson scheme and the 2nd⁃order backward difference scheme for dis⁃cretization in time,respectively,and the barycentric Lagrange interpolation collocation method for discretiza⁃tion in space.Moreover,the approximation properties of the barycentric Lagrange interpolation were presented.Numerical experiments show that the time⁃convergence rates of the 2 types of SAV schemes are of the 2nd order and both schemes satisfy the energy decay law.Compared with the finite difference method in space,the bary⁃centric Lagrange interpolation collocation scheme features exponential convergence.
作者
黄蓉
邓杨芳
翁智峰
HUANG Rong;DENG Yangfang;WENG Zhifeng(School of Mathematical Sciences,Huaqiao University,Quanzhou,Fujian 362021,P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2023年第5期573-582,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金项目(11701197)
中央高校基本科研业务费(ZQN-702)。
