本文构造了求解非线性对流扩散方程的两重网格算法,该算法首先是在步长为H的粗网格上求解一个非线性问题,再利用粗网格解得到一个线性问题并在细网格上求解一个线性问题。理论分析与数值计算表明,该算法不仅消除了数值振荡现象,还极大地提高了非线性对流扩散方程的计算效率。
A two-grid method for numerically solving the nonlinear convection-dominated diffusion problems is presented. This method includes two steps. First,a nonlinear problem is solved on a coarse grid,and then a linear problem generated by the coarse grid solutions is solved on a fine grid. The theoretical analysis and numerical example show that the new method is numerical stable and effcient.