摘要
针对一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,更重要的是可以加快收敛速度、提高计算效率.误差估计表明,只要选取粗网格步长与细网格步长的平方根同阶,就可以使两重网格解与有限元解保持同样的计算精度.
For one dimensional nonlinear convection diffusion equation, a two-grid method of characteristic finite-element solution is constructed, where the nonlinear iteration is only executed on the coarse grid, then the fine-grid solution can be obtained via a single linear step. For the nonlinear convection-dominated diffusion equation, the method can stabilize the numerical oscillation, accelerate the convergence and improve the computational efficiency. The error analysis demonstrates that if the mesh size of coarse-grid equal to the square root of fine-grid, the two-grid solution of the characteristic finite-element and the iteration solution of characteristic finite-element have the same order of accuracy.
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
2004年第2期208-211,共4页
Journal of Xi'an Jiaotong University
基金
国家自然科学基金资助项目 (NSF50 1 1 3 63 0 )
陕西省教育厅自然科学基金资助项目 (0 2JK0 48).
关键词
对流扩散方程
特征有限元
两重网格算法
收敛性
convection-diffusion equation
characteristic finite-element
two-grid method
convergence
