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二阶椭圆问题的一类广义有限元法
引用本文:司红颖,魏先勇,陈绍春.二阶椭圆问题的一类广义有限元法[J].计算数学,2016,38(4):405-411.
作者姓名:司红颖  魏先勇  陈绍春
作者单位:1. 商丘师范学院数学与信息科学学院, 河南商丘 476000;
2. 商丘职业技术学院, 河南商丘 476000;
3. 郑州大学数学系, 郑州 450052
基金项目:国家自然科学基金(No.11371103),青年骨干教师项目资助(No.2014GGJS16)
摘    要:本文提出了求解二阶椭圆问题的一类广义有限元方法,分析了广义有限元方法的优越性,证明了二阶椭圆问题的广义有限元方法具有比标准的Galerkin有限元方法更高阶的收敛速度,根据插值算子的性质,进一步证明了有限元解的亏量迭代校正收敛到广义有限元解,并用数值例子说明广义有限元方法是有效的.

关 键 词:二阶椭圆问题  广义有限元法  亏量迭代
收稿时间:2015-10-26;

A GENERALIZED FINITE ELEMENT METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS
Si Hongying,Wei Xianyong,Chen Shaochun.A GENERALIZED FINITE ELEMENT METHOD FOR SECOND ORDER ELLIPTIC PROBLEMS[J].Mathematica Numerica Sinica,2016,38(4):405-411.
Authors:Si Hongying  Wei Xianyong  Chen Shaochun
Institution:1. School of Mathematics and information Sciences, Shangqiu Normal University, Shangqiu 476000, Henan, China;
2. Shangqiu Polytechnic, Shangqiu 476000, Henan, China;
3. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China
Abstract:In this paper we present a generalized finite element method for solving second order elliptic problems and analyze the superiority of this method. We prove that the generalized finite element method of the second order elliptic problems has higher convergence rate than the standard Galerkin finite element method. And based on the nature of the interpolation operator, we further prove that the defect iterative sequence of the finite element solution converge to the generalized finite element solution. Some numerical examples illustrate the generalized finite element method is effective.
Keywords:second order elliptic problems  a generalized finite element method  defect iteration
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