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Influence of the pollution on the admissible field error estimation for FE solutions of the Helmholtz equation
Author(s) -
Bouillard Ph.
Publication year - 1999
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/(sici)1097-0207(19990710)45:7<783::aid-nme605>3.0.co;2-m
Subject(s) - estimator , helmholtz equation , helmholtz free energy , upper and lower bounds , mathematics , norm (philosophy) , a priori and a posteriori , finite element method , wave equation , elasticity (physics) , mathematical analysis , law , statistics , engineering , physics , philosophy , structural engineering , epistemology , quantum mechanics , political science , thermodynamics , boundary value problem
The a posteriori error estimation in constitutive law has already been extensively developed and applied to finite element solutions of structural analysis problems. The paper presents an extension of this estimator to problems governed by the Helmholtz equation (e.g. acoustic problems) that we have already partially reported, this paper containing informations about the construction of the admissible fields for acoustics. Moreover, it has been proven that the upper bound property of this estimator applied to elasticity problems (the error in constitutive law bounds from above the exact error in energy norm) does not generally apply to acoustic formulations due to the presence of the specific pollution error. The numerical investigations of the present paper confirm that the upper bound property of this type of estimator is verified only in the case of low (non‐dimensional) wave numbers while it is violated for high wave numbers due to the pollution effect. Copyright © 1999 John Wiley & Sons, Ltd.