Gradient recovery in adaptive finite-element methods for parabolic problems

Lakkis, O. and Pryer, T. (2012) Gradient recovery in adaptive finite-element methods for parabolic problems. IMA Journal of Numerical Analysis, 32 (1). pp. 246-278. ISSN 1464-3642 doi: 10.1093/imanum/drq019

Abstract/Summary

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 �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential 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. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.