矩形网格非稳态四阶椭圆方程的质量集中有限元法  

Lumped mass finite element method for fourth order nonsationary elliptic equation on rectangular mesh

作　　者：张斐然[1] 

机构地区：[1]商丘师范学院数学系,河南商丘476000

出　　处：《安徽大学学报（自然科学版）》2011年第1期21-27,共7页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10590353);河南省科技厅自然科学基金资助项目(102300410259);河南省高等学校青年骨干教师基金资助项目

摘　　要：讨论了矩形网格上非稳态四阶椭圆方程的质量集中有限元方法.首先,给出了所讨论问题的质量集中有限元Crank-Nicolson全离散逼近格式.其次,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,在各向异性网格下得到了一定模意义下的一些误差估计.The lumped mass finite element method of fourth order nonsationary elliptic equation was discussed on rectangular meshes. Firistly,we studied the Crank-Nicolson full-discrete approximation scheme of the lumped mass finite element method for the discussed problem. Secondly, error analysis between the solution of the discussed problem and the solution of the approximated scheme were considered. Without using tradtional elliptic projection operator, some error estimations in a certain norm were obtained on anisotropic meshes.

关 键 词：四阶椭圆方程 质量集中 各向异性 矩形网格 全离散 

分 类 号：O241.82[理学—计算数学]