Gradient recovery in adaptive finite element methods for parabolic problems

Omar Lakkis, Tristan Pryer

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
16 Downloads (Pure)

Abstract

We derive energy-norm aposteriori 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 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.
Original languageEnglish
Pages (from-to)246-278
Number of pages32
JournalIMA Journal of Numerical Analysis
Volume32
Issue number1
Early online date10 Jun 2011
DOIs
Publication statusPublished - 31 Jan 2012

Keywords

  • math.NA
  • math.AP
  • 65M60, 65Y20, 65G20

Fingerprint Dive into the research topics of 'Gradient recovery in adaptive finite element methods for parabolic problems'. Together they form a unique fingerprint.

Cite this