二维非线性对流扩散方程特征有限元的两重网络算法

Two-Grid Method for Characteristics Finite-Element Solution of 2D Nonlinear Convection-Dominated Diffusion Problem

针对二维非线性对流扩散方程,构造了特征有限元两重网格算法.该算法只需要在粗网格上进行非线性迭代运算,而在所需要求解的细网格上进行一次线性运算即可.对于非线性对流占优扩散方程,不仅可以消除因对流占优项引起的数值振荡现象,还可以加快收敛速度、提高计算效率.误差估计表明只要选取粗细网格步长满足一定的关系式,就可以使两重网格解与有限元解保持同样的计算精度.算例显示:两重网格算法比特征有限元算法的收敛速度明显加快.

For two dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates ff the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical example confirms that the two-grid method is more efficient than that of characteristics finite-element method.