二阶椭圆方程Dirichlet边值问题混合元的超收敛  

Superconvergence of Mixed Finite Element Methods for Second Order Equation with Dirichlet Boundary Value Problem

作　　者：雷俊丽[1] 林甲富[2] 

机构地区：[1]湖北经济学院经济信息系,湖北武汉430205 [2]北京理工大学理学院数学系,北京100081

出　　处：《应用数学》2005年第S1期180-183,共4页Mathematica Applicata

摘　　要：关于二阶椭圆方程Dirichlet边值问题混合元的超收敛,在正则矩形网格上,林群和林甲富在文[1]中,采用一阶Raviart-Thomas混合元空间,对有限元解经后处理后,其收敛于精确解的速度从二阶提高到四阶.本文拟将这一结果进行推广,讨论二阶椭圆方程Dirichlet边值问题的k阶Raviart-Thomas混合元的超收敛,得到了以k+3阶速度收敛于精确解的有限元解.In [1],Lin Qun and Lin Jiafu has proved that for the 1-th Raviart-Thomas finite element approximation of second order boundary value problem,the convergent rate can be increased from the second order to the fourth order by postprocessing superconvergence technique if the underlying mesh is rectangular and regular.In this paper,we will generalize this conclusion to the k-th Raviart-Thomas mixed finite element,we will see that there exists a (k+3)-th approximation to the equation.

关 键 词：二阶椭圆方程 DIRICHLET边值问题 Raviart-Thomas元 混合有限元 超收敛 后处理 

分 类 号：O175.25[理学—数学]