【摘要】 本文介绍了近年来发展起来的新的有限元的后处理技术—Z-Z小片恢复技术,并探讨了运用Z-Z小片恢复技术对两点边值问题的有限元解的一阶导数进行后处理所产生的超收敛性和后验误差估计.着重在高斯点利用最小二乘拟合技术对于k=1时的一次元和k=2时的二次元的后处理公式进行了推导,得出了后处理公式.并举例验证后处理公式对于两点边值问题-p(u′(x))′+qu(x)=f(x),u(a)=u′(b)=0,x∈[a,b]的正确性。更多还原

【Abstract】 In recent years,a new post-processing technique——Z-Z patch recovery technique has been rapidly developed.This paper discusses the ultraconvergence property and posteriori error estimate of this technique which is used on the one-order derivative of the finite element solution of two-point boundary problem.Then it gives the post-processing formula for k=1 and k=2 by means of fitting in the least-squares sense at Gauss point,and one example of two-point boundary problem:-p(u′(x))′+qu(x)=f(x),u(a)=u′(b)=0,x∈ is given to show the correctness of conclusion.更多还原