一维二阶椭圆型方程组的超收敛二次有限体积元方法  

A Kind of Quadratic Superconvergence Finite Volume Element Method for One Dimensional Second-order Elliptic Equations

作　　者：司倩倩[1] 王同科[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《应用数学》2013年第1期58-66,共9页Mathematica Applicata

基　　金：国家自然科学基金资助项目(11071123)

摘　　要：本文针对二阶椭圆型常微分方程组边值问题提出二次超收敛有限体积元方法,证明格式的H1和L2模误差估计,并给出应力佳点处的梯度超收敛估计.最后,编写计算格式的Fortran程序,用数值算例验证了理论分析的正确性和格式的有效性.In this paper, we present a quadratic superconvergence finite volume element method for systems of ordinary differential equations of second-order elliptic boundary value problems and prove H1 and Lz norm error estimates. Further we give the gradient superconve- rgence estimates at optimal stress points. Finally a numerical example is given to show the correctness of theoretical analysis and the efficiency of the scheme by implementing Fortran codes.

关 键 词：一维二阶椭圆型微分方程组边值问题 二次有限体积元方法 误差估计 超收敛 

分 类 号：O241.82[理学—计算数学]