I. Babuska et al., A-POSTERIORI ESTIMATION OF THE ERROR IN THE RECOVERED DERIVATIVES OF THE FINITE-ELEMENT SOLUTION, Computer methods in applied mechanics and engineering, 150(1-4), 1997, pp. 369-396
This work addresses the accuracy of the solution derivatives which are
recovered by local averaging of the finite element solution. The main
results of the study are: (1) The error in the locally averaged deriv
atives (e.g. the derivatives which are recovered by the Zienkiewicz-Zh
u Superconvergent Patch Recovery (ZZ-SPR) or other similar local recov
eries) can be more than the error in the derivatives computed directly
from the finite element solution, especially in the case of unsmooth
solutions and/or coarse meshes. (2) In order to determine which soluti
on derivatives should be relied upon, the locally averaged ones or the
ones computed directly from the finite element solution, one must be
able to estimate their errors. It is shown that one can obtain indicat
ors of the error in the derivatives recovered by the ZZ-SPR by employi
ng an additional local averaging of the recovered derivatives (recycli
ng of the ZZ-SPR) or by comparing the derivatives computed by the ZZ-S
PR with the derivatives obtained using a different local averaging whi
ch takes into account the character of the exact solution (harmonic av
eraging).