非协调有限元逼近的梯度恢复型后验误差估计（英文）  

A Posteriori Error Estimate of Gradient Recovery Type for Nonconforming Finite Element Approximation

作　　者：徐静[1] 陈晶[2] 

机构地区：[1]扬州工业职业技术学院文理系,江苏扬州225127 [2]江南大学理学院,江苏无锡214028

出　　处：《应用数学》2014年第2期248-257,共10页Mathematica Applicata

基　　金：the Natural Science Foundation of Jiangsu Province(BK20131109)

摘　　要：本文给出二阶椭圆型方程的非协调有限元的梯度恢复型后验误差估计.后验误差估计是在Crouzeix-Raviart非协调有限单元上得到的,并且给出误差的上下界,更进一步可以证明所得的后验误差估计在拟一致网格上是渐近精确的,所以误差估计是可行的、有效的.上界证明过程依赖于"Helmholtz分解",下界证明主要依赖"bubble函数".数值结果验证了理论的正确性.In this paper, we derive gradient recovery type a posteriori error estimate for piecewise linear nonconforming finite element approximation of second order elliptic equations. We show that a posteriori error on the Crouzeix-Raviart nonconforming element and give both upper and lower bounds of the estimates. Moreover it is proved that a posteriori error estimate is also asymptotically exact on the quasi-uniform meshes. The a posteriori error estimates are reliable and efficient. The proof of upper bounds relies on a Helmholtz decomposition, and low bounds relies on bubble function. The numerical results demonstrating the theoretical results are also presented in this paper.

关 键 词：非协调 Crouzeix—Raviart元 后验误差估计 梯度恢复 

分 类 号：O241.8[理学—计算数学]