摘要
采用与传统Raviart-Thomas(R-T)元方法不同的变分形式,对Sobolev方程提出了最低阶的半离散和全离散混合有限元格式.借助双线性元及零阶R-T元已有的高精度分析及平均值技巧,分别导出了精确解u的H^1模和中间变量p的L^2模超逼近性质和整体超收敛结果.数值结果验证了理论分析的正确性.
In this paper,the lowest mixed finite element methods are proposed for Sobolev equation by employing a different mixed variational form from traditional Raviart-Thomas（R-T） element method for semi-discrete and fully discrete schemes.With the help of the known high accuracy analysis of the bilinear element and zero order R-T element and mean-value technique,the superclose properties and the global superconvergence results of exact solution u in H^1-norm and intermediate variable p in L^2-norm are deduced.Numerical results show the correctness of the theoretical analysis.
出处
《系统科学与数学》
CSCD
北大核心
2014年第4期452-463,共12页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(11101381
11271340)
河南省高等学校青年骨干教师资助项目(2011GGJS-182)
河南省教育厅自然科学基金(13A110741)
许昌市科技计划(5015
5016)资助课题
关键词
SOBOLEV方程
混合元方法
半离散和全离散
超逼近和整体超收敛
Sobolev equation
mixed finite element method
semi-discrete and fullydiscrete schemes
superclose properties and superconvergence.
