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Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates
Author(s) -
Díez Pedro,
Parés Núria,
Huerta Antonio
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.620
Subject(s) - residual , estimator , upper and lower bounds , a priori and a posteriori , simple (philosophy) , mathematics , standard error , error detection and correction , error analysis , work (physics) , yield (engineering) , mathematical optimization , algorithm , computer science , statistics , mathematical analysis , engineering , mechanical engineering , philosophy , materials science , epistemology , metallurgy
Classical residual type error estimators approximate the error flux around the elements and yield upper bounds of the exact (or reference) error. Lower bounds of the error are also needed in goal oriented adaptivity and for bounds on functional outputs. This work introduces a simple and cheap strategy to recover a lower bound estimate from standard upper bound estimates. This lower bound may also be used to assess the effectivity of the former estimate and to improve it. Copyright © 2003 John Wiley & Sons, Ltd.