摘要
标准的两重网格方法是一种求解二阶椭圆问题的局部并行方法,其计算所得数值解在整个求解区域上并不连续.使用单位分解技术,将各个子区域上的局部解粘合在一起,从而得到全局连续解,并证明此解在H1范数意义下最优.更进一步,可以证明通过在粗网格上修正,能够改善其L2误差.数值例子验证了理论的正确性.
A two-grid partition of unity method for second order elliptic problems was proposed and analyzed. The standard two-grid method is a local and parallel method which usually leads to a discontinuous solution in the whole computational donmain. Partition of unity method was employed to glue all the local solutions together to get global continuous one, which is optimal in Hl-norm. Furthermore, it is shown that theL2 error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theory.
出处
《应用数学和力学》
EI
CSCD
北大核心
2008年第4期477-482,共6页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(40074031)
上海市科学技术委员会基金资助项目
关键词
二阶椭圆问题
两重网格方法
单位分解
second order elliptic problems
two-grid method
partition of unity
