二维非线性对流扩散方程的特征混合有限元两重网格算法  

Two-grid Method for the Characteristic Mixed Finite Element Approximations of 2D Nonlinear Convection Diffusion Problems

作　　者：秦新强[1] 党发宁[2] 龚春琼[1] 张爱君[1] 

机构地区：[1]西安理工大学理学院,西安710048 [2]西安理工大学水利水电学院,西安710048

出　　处：《工程数学学报》2009年第5期906-916,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(50679073);陕西省教育厅自然科学研究项目(08JK399);西安理工大学校基金(108-210711;108-210713)

摘　　要：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.

关 键 词：对流扩散方程 特征混合有限元 两重网格法 收敛性 

分 类 号：O241.82[理学—计算数学]