  Local modifications of a computational domain are often performed in order to
simplify the meshing process and to reduce computational costs and memory
requirements. However, removing geometrical features of a domain often
introduces a non-negligible error in the solution of a differential problem in
which it is defined. In this work, we extend the results from [1] by studying
the case of domains containing an arbitrary number of distinct Neumann
features, and by performing an analysis on Poisson's, linear elasticity, and
Stokes' equations. We introduce a simple, computationally cheap, reliable, and
efficient a posteriori estimator of the geometrical defeaturing error.
Moreover, we also introduce a geometric refinement strategy that accounts for
the defeaturing error: Starting from a fully defeatured geometry, the algorithm
determines at each iteration step which features need to be added to the
geometrical model to reduce the defeaturing error. These important features are
then added to the (partially) defeatured geometrical model at the next
iteration, until the solution attains a prescribed accuracy. A wide range of
two- and three-dimensional numerical experiments are finally reported to
illustrate this work.
