一维Ritz有限元EEP超收敛位移计算简约格式的直接推导与证明

一维Ritz有限元后处理超收敛计算的EEP(单元能量投影)法简约格式中,若问题和解答足够光滑,其m(1)次单元的超收敛位移解在单元内任一点均可以达到至少hm+2的超收敛阶。对此,本文提出一套全新的推证方法,通过对单元能量投影的等效变形,直接推导出EEP简约格式位移解的计算公式及其误差项,进而采用更为简单通用的数学证明方法,证明了这一超收敛性。

A direct derivation and proof of super-convergence of EEP displacement of simplified form in one-dimensional Ritz FEM

For one-dimensional Ritz Finite Element Method (FEM),when both the problems and solutions are sufficiently smooth,the super-convergent displacement from the simplified form of the Element Energy Projection (EEP) method is capable of producing a convergence order of h^m+2 at any point on an element for elements of degree m(>1) in post-processing super-convergence stage of the FEM. Based on the transformation of two equivalent forms of the EEP,both the computational formula and the error term of EEP displacement solution of the simplified form are derived directly,and then its convergence orders are estimated. As a result,a new method has been developed for the mathematical derivation and proof of the super-convergence of EEP displacement of the simplified form.