摘要
最近,袁驷等基于力学原理提出了一种一维有限元超收敛后处理计算格式,称为单元能量投影(EEP)法。大量数值例子显示:若真解充分光滑,对m次有限元解,EEP法后处理节点恢复导数具有h2m阶精度。首先利用限元超收敛理论中的一个基本估计式证明了线性元(m=1)节点恢复导数具有h2阶精度。另外,对EEP法高次元的内点计算公式提出了一点简化。
Recently, based on mechanics principle, Yuan＇s group proposed a one-dimensional finite element superconvergent postprocessing scheme-Element-Energy-Projection （EEP） method. A large number of numerical examples show that, provided that the exact solution is sufficiently smooth, the EEP method nodal recovery stress have the accuracy of O（h2m） for elements with m degrees-of-freedom. Using a fundamental estimation formula, the linear element nodal recovery stress is firstly proved to have the accuracy of O（h2） by the EEP method. Secondly, a simplification of EEP method for the calculation of higher order element＇s interior point is pointed out.
出处
《工程力学》
EI
CSCD
北大核心
2008年第2期93-94,101,共3页
Engineering Mechanics
基金
湖南大学科学基金项目(521101861)
国家自然科学基金项目(10571046
10371038)
关键词
超收敛
应力恢复
有限元
单元能量投影法
一维问题
superconvergence
stress recovery
finite element
element energy projection
one dimensional problem
