双线性非协调有限元逼近的梯度恢复后验误差估计  

Gradient Recovery Type a Posteriori Error Estimate for Bilinear Nonconforming Finite Element Approximation

作　　者：徐静[1] 周俊明[2] 邓光[1] 刘长太[1] 

机构地区：[1]扬州工业职业技术学院基础部,江苏扬州225127 [2]河北工业大学数学系,天津300000

出　　处：《数学的实践与认识》2010年第16期113-120,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(NSFC10471103)

摘　　要：给出了二阶椭圆方程的双线性非协调有限元逼近的梯度恢复后验误差估计.该误差估计是在Q_1非协调元上得到的,并给出了误差的上下界.进一步证明该误差估计在拟一致网格上是渐进精确地.证明依赖于clement插值和Helmholtz分解,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 bilinear nonconforming finite element approximation of second order elliptic equations.We show that a posteriori error on the Q1 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 reliability relies on a weak interpolation operator due to Clement and a Helmholtz decomposition.The numerical results demostrating the theoretical results are also presented in this paper.

关 键 词：非协调 后验误差估计 梯度恢复 渐进精确 

分 类 号：O241.82[理学—计算数学]