一维Ritz有限元超收敛计算的EEP法简约格式的误差估计

AN ERROR ESTIMATE OF EEP SUPER-CONVERGENT SOLUTIONS OF SIMPLIFIED FORM IN ONE-DIMENSIONAL RITZ FEM

该文对一维0C问题Ritz有限元后处理超收敛计算的EEP(单元能量投影)法简约格式给出误差估计的数学证明,即对足够光滑问题的m(>1)次单元的有限元解答,采用EEP法简约格式计算得到的单元内任一点位移和应力(导数)超收敛解均可以达到m2h?的收敛阶,即位移比常规有限元解的收敛阶至少高一阶,而应力则至少高二阶。

For one-dimensional0 C problems of Ritz Finite Element Method(FEM), an error estimate is presented for the simplified form of the Element Energy Projection(EEP) method used for super-convergence computation in post-processing stage of FEM. The mathematical analysis proves that for elements of degree m(>1) with sufficiently smooth solutions, EEP solutions of the simplified form are capable of producing super-convergent solutions with convergence order ofm2h?for both displacements and stresses at any point on an element, i.e. EEP simplified form obtains at least one order higher displacements and at least two order higher stresses than conventional FEM solutions.