Gradient recovery in adaptive finite-element methods for parabolic problems

摘要

We derive energy-norm a posteriori error bounds using gradient recovery (ZZ) estimators to control the spatial error for fully discrete schemes for the linear heat equation. This appears to be the first completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems without any restrictive assumption on the time-step size. Anessential tool for the analysis is the elliptic reconstruction technique. Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error and (b) deriving an adaptive method based on our estimators.