Allen-Cahn方程的非协调元二重网格方法的超收敛分析  

Superconvergence Analysis of a Two-grid Method with Nonconforming Element for Allen-Cahn Equation

作　　者：石东洋 位一凡 SHI Dongyang;WEI Yifan(School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]郑州大学数学与统计学院,河南郑州450001

出　　处：《信阳师范学院学报（自然科学版）》2020年第2期173-180,共8页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671369)。

摘　　要：利用EQ1^rot非协调有限元对Allen-Cahn方程建立一个关于时间有二阶精度的二重网格算法.借助于单元的特殊性质、导数转移技巧和插值后处理技术,在离散的H^1模意义下得到了O(h^2+H^4+τ^2)阶的超逼近和超收敛结果.给出了数值算例以验证理论的正确性与算法的高效性.这里h、H和τ分别表示细网格、粗网格的剖分尺度和时间步长.A second order two-grid algorithm for Allen-Cahn equation is developed by using the nonconforming EQ1^rot finite element.Based on the special properties of this element,the derivative transfer technique and the interpolated postprocessing approach,the superclose and superconvergence results of order O(h^2+H^4+τ^2)in the broken H^1-norm are deduced.A numerical example is given to verify the theoretical predictions and to show the efficiency of the proposed method.Here,h,H andτrepresent the mesh size of fine grid,mesh size of coarse grid and time step size,respectively.

关 键 词：Allen-Cahn方程 EQ^rot1非协调元 二阶精度二重网格 导数转移和插值后处理 超逼近和超收敛结果 

分 类 号：O242.21[理学—计算数学]