双曲型方程的质量集中全离散非协调元方法  

The lumped mass full-discrete nonconforming finite element method for hyperbolic equation

作　　者：张斐然[1] 宋益荣[2] 

机构地区：[1]商丘师范学院数学系,河南商丘476000 [2]商丘职业技术学院数学系,河南商丘476000

出　　处：《安徽大学学报（自然科学版）》2012年第6期5-10,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10590353);河南省基础与前沿技术研究计划基金资助项目(102300410259)

摘　　要：在各向异性网格下,讨论了双曲型方程的质量集中非协调有限元Crank-Nicolson全离散逼近格式,对讨论问题的解与逼近格式的解之间的误差进行了分析.不需要传统的椭圆投影算子,利用一些新的技巧和单元的特殊性质得到了L2模和能量模的最优误差估计.In the paper, the Crank-Nicolson full-discrete approximation scheme of the lumped mass nonconforming finite element method for hyperbolic equation was discussed on anisotropic meshes, error analysis between the solution of the discussed problem and the solution of the approximated scheme were considered. Without using traditional elliptic projection operator, the optimal error estimations of L2-norm and energy-norm were obtained based on some novel techniques and special properties of the elements.

关 键 词：质量集中 全离散 各向异性 双曲型方程 Crank—Nicolson格式 

分 类 号：O241.82[理学—计算数学]