Influence of the pollution on the admissible field error estimation for Fesolutions of the Helmholtz equation

The a posteriori error estimation in constitutive law has already been exte nsively developed and applied to finite element solutions of structural ana lysis problems. The paper presents an extension of this estimator to proble ms governed by the Helmholtz equation (e.g. acoustic problems) that we have already partially reported, this paper containing informations about the c onstruction of the admissible fields for acoustics. Moreover, it has been p roven 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 th e presence of the specific pollution error. The numerical investigations of the present paper confirm that the upper bound property of this type of es timator 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. Cop yright (C) 1999 John Wiley & Sons, Ltd.