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Guaranteed computable error bounds for conforming and nonconforming finite element analyses in planar elasticity
Author(s) -
Ainsworth Mark,
Rankin Richard
Publication year - 2010
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.2799
Subject(s) - estimator , finite element method , mathematics , norm (philosophy) , a priori and a posteriori , elasticity (physics) , upper and lower bounds , planar , mathematical analysis , computer science , statistics , physics , computer graphics (images) , thermodynamics , philosophy , epistemology , political science , law
Abstract We obtain fully computable a posteriori error estimators for the energy norm of the error in second‐order conforming and nonconforming finite element approximations in planar elasticity. These estimators are completely free of unknown constants and give a guaranteed numerical upper bound on the norm of the error. The estimators are shown to also provide local lower bounds, up to a constant and higher‐order data oscillation terms. Numerical examples are presented illustrating the theory and confirming the effectiveness of the estimator. Copyright © 2009 John Wiley & Sons, Ltd.