一维有限元后处理的EEP法的数学分析

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基金项目: 国家自然科学基金资助项目(10571046;10371038)

Mathematical Analysis of EEP Method for One-Dimensional Finite Element Postprocessing

College of Mathematics and Economatics, Hunan University, Changsha 410082, P. R. China;

摘要: 利用一维投影型插值与有限元超收敛基本估计，对一类两点边值问题，严格证明了袁驷等人由单元能量投影(EEP)法获得的节点恢复导数，当有限元空间的次数不超过4时，具有最佳阶超收敛．理论分析圆满地解释了已有的数值结果．
- 超收敛应力 /
- 单元能量投影法 /
- 有限元 /
- 两点边值问题 /
- 投影型插值
Abstract: Fora class of two-point boundary value problems, by virtue of one-dimensional projection interpolation and finite element superconvergence fundamental estimations, it was proved that the nodal recovery derivative obtained by Yuan's element energy projection (EEP) method had the optimal order superconvergence on condition that the degree of finite element space is no more than 4. The theoretical analysis coincides with the reported numerical results.
- superconvergence stress /
- element energy projection method /
- finite element /
- two-point boundary value problems /
- projection interpolation

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