Lakkis, Omar and 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.
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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.
|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:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics|
|Depositing User:||Tristan Pryer|
|Date Deposited:||05 Oct 2012 15:12|
|Last Modified:||28 Jan 2013 12:19|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/31255 (The current URI for this page, for reference purposes)|
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