泊松方程及平面弹性问题有限元方法中求高阶导数的提取法

在许多有限元计算中经常在求得近似解后还要求得到近似的解的导数.如在弹性计算中,如何从计算得到的位移近似解较好地计算应力早已被研究多年.如果计算中包含直接对近似解求导数,必然会丧失部分精度,得不到满意的结果.特别,若近似解为分片常数函数,则根本无法从直接求导数得到应力的近似值.Babuska和 Miller提出了所谓“提取法”,即利用推导出来的提取公式来求解的导数的近似值,以得到与近似解本身同

EXTRACTION OF HIGHER DERIVATIVES IN FEM FOR POISSON EQUATION AND THE PLANE ELASTICITY PROBLEM

This paper gives extraction formulae for higher derivatives of solutions of thePoisson equation and the plane elasticity problem. With these formulae the approxi-mation of higher derivatives of solution obtained from the finite element solutionhas the same order of accuracy as for the approximate solution itself. These resultscan be used in a-posteriori error estimates and the adaptive finite element methods.