摘要
§1.引言
对流扩散方程描述了众多的物理现象,其数值算法研究一直受到重视[1～6,13～14].在这方面,特征差分方法和特征有限元方法是非常有效的两种方法[1～6].特征差分方法计算简单,但适应区域不够灵活.
This paper presents two characteristic difference schemes on triangular mesh for two-dimensional linear and nonlinear convection-diffusion equations. It is proved that the two methods satisfy discrete maximum principle and they are stable in discrete maximum norm. It is also proved that they converge in discrete maximum norm and the first one has first order accuracy for convection term and the other has second order accuracy for convection term, which is especially suitable for solving strong convection-dominated diffusion problems. Finally, numerical examples show that these methods are very effective for solving convection-dominated diffusion problems.
出处
《数值计算与计算机应用》
CSCD
北大核心
2003年第3期177-188,共12页
Journal on Numerical Methods and Computer Applications
基金
国家自然科学基金(项目编号:19972039)
