Sobolev方程新混合元方法的高精度分析  

HIGH ACCURACY ANALYSIS OF A NEW MIXED FINITE ELEMENT METHOD FOR SOBOLEV EQUATION

作　　者：史艳华[1] 石东洋[2] 

机构地区：[1]许昌学院数学与统计学院,许昌461000 [2]郑州大学数学与统计学院,郑州450052

出　　处：《系统科学与数学》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

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.

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 

分 类 号：O241.82[理学—计算数学]