Journal Article

Gradient recovery in adaptive finite-element methods for parabolic problems

Omar Lakkis and Tristan Pryer

in IMA Journal of Numerical Analysis

Published on behalf of Institute of Mathematics and its Applications

Volume 32, issue 1, pages 246-278
Published in print January 2012 | ISSN: 0272-4979
Published online June 2011 | e-ISSN: 1464-3642 | DOI: http://dx.doi.org/10.1093/imanum/drq019
Gradient recovery in adaptive finite-element methods for parabolic problems

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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.

Keywords: adaptive methods; a posteriori estimates; averaging operators; finite elements; gradient recovery; parabolic problems

Journal Article.  0 words. 

Subjects: Mathematics

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