  An a posteriori error estimator based on an equilibrated flux reconstruction
is proposed for defeaturing problems in the context of finite element
discretizations. Defeaturing consists in the simplification of a geometry by
removing features that are considered not relevant for the approximation of the
solution of a given PDE. In this work, the focus is on Poisson equation with
Neumann boundary conditions on the feature boundary. The estimator accounts
both for the so-called defeaturing error and for the numerical error committed
by approximating the solution on the defeatured domain. Unlike other estimators
that were previously proposed for defeaturing problems, the use of the
equilibrated flux reconstruction allows to obtain a sharp bound for the
numerical component of the error. Furthermore, it does not require the
evaluation of the normal trace of the numerical flux on the feature boundary:
this makes the estimator well-suited for finite element discretizations, in
which the normal trace of the numerical flux is typically discontinuous across
elements. The reliability of the estimator is proven and verified on several
numerical examples. Its capability to identify the most relevant features is
also shown, in anticipation of a future application to an adaptive strategy.
