摘要
考虑一类非守恒形式的对流扩散边值问题.为了对其数值求解,采用移动网格方法,使用了两种迎风差分格式(一般迎风格式和中点迎风格式).采用的网格有(N+1)个节点并初始化为均匀网格,其节点采用一种迭代算法来自适应移动,该算法等分布分片线性数值解函数弧长.用数值试验证实了该方法产生的数值解是关于摄动参数ε一阶一致收敛的,从而表明了方法的精确性.
In this paper,we consider a nonconservative convection-diffusion boundary value problem.To solve it numerically, we use a moving mesh method,two upwind difference discretizations ( simple upwind scheme and midpoint upwind scheme ) are applied.The mesh used has a fixed number (N+1) of nodes and is initially uniform,but its nodes are moved adaptively using an iterative algorithm based on equidistribution of the arc-length of the current computed piecewise linear solution.A lot of numerical computations are used to testify that the numerical solutions computed by our method are first-order uniformly convergent with respect to the perturbation parameter ε, which demonstrate the accuracy of the method.
出处
《湘潭大学自然科学学报》
CAS
CSCD
2004年第3期24-29,共6页
Natural Science Journal of Xiangtan University
基金
国家自然科学基金资助项目(10371104)
关键词
一致收敛
奇异摄动
迎风差分格式
移动网格
等分布
uniform convergence
singularly perturbed
upwind difference approximation
moving mesh
equidistribution
