奇异摄动反应扩散方程的后验误差估计及自适应算法  

A Posteriori Error Estimation and Adaptive Algorithm for Singularly Perturbed Reaction-Diffusion Equations

作　　者：包小兵 刘利斌 毛志 BAO Xiaobing;LIU Libin;MAO Zhi(School of Big Data and Artificial Intelligence,Chizhou University,Chizhou,Anhui 247000,P.R.China;School of Mathematics and Statistics,Nanning Normal University,Nanning 530100,P.R.China;School of Data Science,Tongren University,Tongren,Guizhou 554300,P.R.China)

机构地区：[1]池州学院大数据与人工智能学院,安徽池州247000 [2]南宁师范大学数学与统计学院,南宁530100 [3]铜仁学院大数据学院,贵州铜仁554300

出　　处：《应用数学和力学》2021年第3期323-330,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11761015);广西自然科学基金(2017GXNSFBA198183);广西自然科学基金(重点项目)(2017GXNSFDA198014,2018GXNSFDA050014);贵州省教育厅创新群体重大研究项目(KY[2016]051);中国博士后科学基金(面上项目)(2017M623074);2018年贵州省科技基金(一般项目)([2018]1162)。

摘　　要：研究了一类奇异摄动半线性反应扩散方程的自适应网格方法.在任意非均匀网格上建立迎风有限差分离散格式,并推导出离散格式的后验误差界,然后用该误差界设计自适应网格移动算法.数值实验结果证明了所提出的自适应网格方法的有效性.An adaptive grid method for singularly perturbed semilinear reaction-diffusion equations was studied.The equation was discretized by means of the upwind finite difference scheme on an arbitrary nonuniform mesh.A posteriori error estimation of the presented numerical scheme was built.In turn,the posteriori error bound was derived,and the adaptive grid generation algorithm was designed.Numerical experiments prove the effectiveness of the proposed adaptive grid method.

关 键 词：奇异摄动 后验误差 自适应移动网格 反应扩散方程 

分 类 号：O241.81[理学—计算数学]