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

The a posteriori error estimation in constitutive law has already been extensively developed and applied to "nite 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 "elds 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 speci"c pollution error. The numerical investigations of the present paper con"rm that the upper bound property of this type of estimator is veri"ed only in the case of low (non-dimensional) wave numbers while it is violated for high wave numbers due to the pollution e!ect.