摘要
本文研究了二维扩散方程九点格式中节点辅助未知量的插值问题.利用多点通量逼近的边未知量插值算法和一个特殊的极限技巧,获得了节点辅助未知量的一个新的插值算法,并在给定假设下严格分析了该算法中局部线性系统的可解性.新算法满足线性精确准则,具有较高的精度.
In this paper,we discuss the interpolation problem for nodal auxiliary unknowns in nine point scheme for 2D diffusion problems.By applying a special limit technique to the edge interpolation algorithm in multipoint flux approximation,we obtain a new nodal interpolation algorithm.Moreover,the solvability of the local system in the interpolation algorithm is analyzed rigorously under certain assumptions.The new algorithm satisfies linearity preserving criterion and has a second-order accuracy.
作者
董成
邬吉明
DONG Cheng;WU Ji-ming(Graduate School of China Academy of Engineering Physics,Beijing 100088,China;Institute of Applied Physics and Computational Mathematics,Beijing 100088,China)
出处
《数学杂志》
2019年第2期203-215,共13页
Journal of Mathematics
基金
国家自然科学基金资助(11271053
11671313)
关键词
扩散方程
九点格式
节点未知量插值
线性精确
diffusion equation
nine point scheme
nodal interpolation algorithm
linearity preserving
