一类奇异摄动对流扩散方程组的自适应网格方法的收敛性分析  

Convergence Analysis of an Adaptive Grid Method for a System of Singularly Perturbed Convection Diffusion Equations

作　　者：包小兵 方虹淋 刘利斌 BAO Xiaobing;FANG Honglin;LIU Libin(School of Big Data and Arti cial Intelligence,Chizhou University,Chizhou 247000,China;School of General Education,Chongqing Institute of Engineering,Chongqing 400900,China;School of Mathematics and Statistics,Nanning Normal University,Nanning 530023,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]重庆工程学院通识学院,重庆400900 [3]南宁师范大学数学与统计学院,广西南宁530023

出　　处：《应用数学》2021年第1期184-193,共10页Mathematica Applicata

基　　金：国家自然科学基金(11761015);广西自然科学基金(2020GXNSFAA159010);广西自然科学基金重点项目(2017GXNSFDA198014,2018GXNSFDA050014);池州学院自然科学重点项目基金(CZ2018ZR06);池州学院校级教学团队(2018XJXTD03)。

摘　　要：基于经典的迎风有限差分方法,本文讨论一类奇异摄动对流扩散方程组的自适应网格算法.首先,利用Taylor级数展开,给出离散格式的局部截断误差估计.然后,利用等分布原理和极大值原理,证明基于弧长控制函数的自适应网格算法是一阶收敛的.最后的数值实验验证了本文的理论结果.Based on the classical upwind finite difference scheme,an adaptive grid algorithm for a system of singularly perturbed convection-diffusion equations is discussed.At first,by using Taylor series expansion,the local truncation error of this discrete scheme is given.Then,by utilizing the equidistribution principle and maximum principle,we prove that the convergence order of the adaptive grid based on arclength monitor function is first-order.Finally,the numerical results are provided to illustrate the presented theoretical result.

关 键 词：奇异摄动 局部截断误差 迎风有限差分格式 自适应算法 

分 类 号：O241.8[理学—计算数学]