平面弹性振动模型的时空非协调有限元分析  

The space-time nonconforming finite element analysis for the vibration model of plane elasticity

作　　者：成磊峰[1] 韩波[1] 谢小平[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2012年第2期258-266,共9页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(10771150)

摘　　要：本文针对平面弹性的振动模型,提出了一种新的时空有限元方法.在时间和空间方向上,分别采用连续的分片二次多项式插值和非协调不完全二次矩形有限元来离散位移.作者证明了能量范数下相应的误差阶为O(h^(1/2)+k^3),其中h和k分别表示网格剖分的空间尺度和时间尺度.数值算例验证了理论结果.In this paper,a new space-time finite element method is proposed for the vibration model of plane elasticity. In the time and space directions,the authors adopt respectively the continuous piecewise quadratic polynomials interpolation and a nonconforming rectangle finite element to discretize the displacement. They prove that the error estimate of the method in the energy norm is O（h^l/2 ＋k^3） ,where h and k denote the mesh parameters of the subdivisions in the space and time directions,respectively. Nu merical results are included to verify the theoretical results.

关 键 词：平面弹性振动模型 时空非协调有限元 误差估计 

分 类 号：O242.21[理学—计算数学]