Stokes问题有限元逼近中求导数的提取法

1.引言 我们知道Poisson方程和平面弹性问题的解的导数的近似值可以通过所谓提取公式得到,而不必对近似解直接求导数.这样我们可以得到具有与近似解本身同阶精度的导数的近似值.这一方法已被用于基于插值误差的后验误差估计及相应的自适应有限元方法中本文将这一方法应用于Stokes问题的有限元逼近,从Stokes方程的解的

EXTRACTION METHODS FOR DERIVATIVES IN FINITE ELEMENT APPROXIMATIONS OF STOKES PROBLEM

This paper gives extraction formulae tor first, second and third derivatives ofsolutions of the Stokes problem. By use of these formulae, the approximation ofderivatives of solutions obtained from finite element solutions has the same orderof accuracy as the approximation of the solutions themselves. These formulae canbe used in adaptive finite element methods for solving the Stokes problem.