摘要
本文讨论Poisson方程Dirichlet边值问题并证明了在拟一致矩形剖分下双线性有限元解的超收敛性质与外推估计,井由此得出非协调的Wilson有限元的相应性质。接着本文还证明了双二次有限元在拟一致剖分下超收敛性及高阶误差渐近展开。本文的结果包含了文[5]的结论,同时推广了[1]、[6]的结果。
In this paper, the extrapolation estimats of bilinear finite element and wilson's nonconforminf finite element approximations are shown forDirichlet problems of possion equation under quasi-uniforming rectangularmeshes. A superconvergence estimate of biquadratic finite element solutionare also proved under same meshes. Furthermore, for uniforming meshesthe approximation error of biquatratic element can be expanded in theform u(z) - u_2~h(z)=w(z)h^4 + O(h^e|Lnh|)at the vertices of all elements of the meshes.
出处
《湘潭大学自然科学学报》
CAS
CSCD
1989年第4期1-11,共11页
Natural Science Journal of Xiangtan University
基金
国家自然科学基金
关键词
双线性元
超收敛
矩形剖分
有限元
quas-uniforming rectangular meshes
bilinear finite element
wilson element
biquadratic element
superconvergence
extrapo-lation
