一类强耦合的奇异摄动对流扩散方程组的移动网格方法（英文）  

A Moving Grid Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems

作　　者：毛志[1] 刘利斌 MAO Zhi;LIU Libin(Department of Mathematics and Statistics, Tongren University, Tongren 554300, China;School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning 530023, China;Guangxi Colleges and Universities Key Laboratory of Data Science, Nanning 530023, China)

机构地区：[1]铜仁学院数学与统计系,贵州铜仁554300 [2]广西师范学院数学与统计科学学院,广西南宁530023 [3]广西高校数据科学重点实验室,广西南宁530023

出　　处：《应用数学》2018年第3期653-660,共8页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11761015);the Natural Science Foundation of Guangxi(2017GXNSFBA198183);the Key Project of Guangxi Natural Science Foundation(2017GXNSFDA198014);the Guizhou Provincial Cooperation Project in Science and Technology(Project No.LH[2015]7247);the Dr.Scientific Research Starting Foundation of Tongren University(Grant No.trxy DH1526)

摘　　要：本文研究一类强耦合的奇异摄动对流扩散方程组的移动网格方法.首先,利用迎风有限差分格式对方程组进行离散.然后,推出数值解的后验误差估计,并以此设计出相应的自适应网格生成算法.同时,证明数值解具有一阶一致收敛性.最后,数值实验验证了本文移动网格方法的一致收敛性.In this paper, a system of strongly coupled singularly perturbed convectiondiffusion problems is considered. Firstly, an upwind finite difference scheme is applied to discrete this system. Then, an a posteriori error estimate in the maximum norm is obtained which is used to design an adaptive grid generation algorithm. Finally, a first-order rate of convergence, independent of the perturbation parameters, is proved. Numerical results are given to confirm the uniform convergence rate of the nodal errors.

关 键 词：一致收敛 奇异摄动 强耦合 迎风有限差分格式 

分 类 号：O241.8[理学—计算数学]