对流扩散方程的迎风广义差分格式

UPWIND GENERALIZED DIFFERENCE SCHEMES FOR CONVECTION-DIFFUSION PROBLEMS

一、引言 考虑对流扩散方程的稳态问题 ?这里Ω为R^2上的有界凸域,Ω为其光滑围道;a为常数,c(x)为上的光滑函数,b(x)=(b_1(x),b_2(x))为上的光滑向量函数,并且满足 |b(x)|>>a>0,c(x)≥0,c(x)-divb(x)≥0,x∈.一般情况下,方程(1)的解u(x)在一窄层内迅速变化,用通常的差分法或有限元法计算,将产生严重的振荡失真现象.本文基于广义差分法构造了一类新的迎风格式。

In this paper, we propose a class of upwind schemes for the convection-diffusion pro-blems based on generalized difference methods [1],[2]. For the steady-state problem, themaximum principle and the uniform convergence are obtained.