Two-Grid Method for Characteristics Finite-Element Solution of 2D Nonlinear Convection-Dominated Diffusion Problem
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摘要: 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．Abstract: 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 convection-dominated 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 if 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.
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