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Gradient recovery in adaptive finite-element methods for parabolic problems

Lakkis, Omar, Pryer, Tristan (2012) Gradient recovery in adaptive finite-element methods for parabolic problems. IMA Journal of Numerical Analysis, 32 (1). pp. 246-278. ISSN 0272-4979. (doi:10.1093/imanum/drq019) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31255)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL:
http://dx.doi.org/10.1093/imanum/drq019

Abstract

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.

Item Type: Article
DOI/Identification number: 10.1093/imanum/drq019
Uncontrolled keywords: adaptive methods; a posteriori estimates; averaging operators; finite elements; gradient recovery; parabolic problems
Subjects: Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: T.M. Pryer
Date Deposited: 05 Oct 2012 15:12 UTC
Last Modified: 16 Nov 2021 10:09 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/31255 (The current URI for this page, for reference purposes)

University of Kent Author Information

Pryer, Tristan.

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