摘要
针对Poisson方程Dirichlet边值问题,首先建立了四维投影型插值算子,并应用它得到了正规剖分下四维张量积二次矩形有限元的弱估计,在此基础上,结合四维离散Green函数的估计,研究四维张量积二次矩形有限元解及梯度最大模的超逼近,获得了逐点意义下高精度的超收敛结果.
For Dirichlet boundary value problems of Poisson equations, an interpolation operator of projection type in 4D was established. Then by using this operator, weak estimates for tensor-product quadratic rectangular finite elements over regular partitions of a domain were obtained. Based on the obtained results and the estimates for the four- dimensional discrete Green＇s function, some highly accuracy results of the maximum-norm superapproximations of finite elements were derived.
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2011年第4期134-141,共8页
Journal of East China Normal University(Natural Science)
基金
湖南省高等学校科学研究一般项目(10C0913)
关键词
椭圆边值问题
四维投影型插值算子
矩形有限元
弱估计
超逼近
elliptic boundary value problem
interpolation operator of projection type in 4D
rectangular finite element
weak estimate
superapproximation
