二阶椭圆问题带单位分解技巧的两重网格方法  

Two-Grid Partition of Unity Method for Second Order Elliptic Problems

作　　者：王琤[1] 黄自萍[2] 李立康[3] 

机构地区：[1]同济大学数学系,上海 200092 [2]同济大学中德学院,上海 200092 [3]复旦大学数学系,上海 200433

出　　处：《应用数学和力学》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

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.

关 键 词：二阶椭圆问题 两重网格方法 单位分解 

分 类 号：O242.21[理学—计算数学] O246[理学—数学]