摘要
对基于两重网格的非定常对流扩散方程的局部和并行有限元算法进行了研究.算法的理论依据是两重网格的思想,解的低频分量可以用一个整体的粗网格空间来逼近,高频分量可以用局部和并行的细网格空间来逼近.因此,这种局部和并行算法仅仅涉及一个粗网格上的整体逼近和细网格上的局部校正.得到了算法的误差估计,一些数值例子验证了算法的有效性.
Local and parallel finite element algorithms based on two-grid discretization for the timedependent convection-diffusion equations are presented. These algorithms are motivated by the observation that for a solution to the convection-diffusion problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure. Hence, these local and parallel algorithms only involve one small original problem on coarse mesh and some correction problems on local fine grid. One technical tool for the analysis is some local a priori estimates that are also obtained. Finally, some numerical examples are given to support our theoretical analysis.
出处
《应用数学和力学》
CSCD
北大核心
2009年第6期733-740,共8页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(10871156)
新世纪优秀人才支持计划资助项目(NCET-06-0829)
关键词
局部和并行算法
有限元法
对流扩散方程
local and parallel algorithm
finite dement method
convection-diffusion equation
