  The era of detailed asteroseismic analyses opened by space missions such as
CoRoT and $\textit{Kepler}$ has highlighted the need for stellar models devoid
of numerical inaccuracies, in order to be able to diagnose which physical
aspects are being ignored or poorly treated in standard stellar modeling. We
tackle here the important problem of fixing convective zones boundaries in the
frame of the local mixing length theory. First we show that the only correct
way to locate a convective zone boundary is to find, at each iteration step,
through interpolations or extrapolations from points $\textit{within the
convective zone}$, the mass where the radiative luminosity is equal to the
total one. We then discuss two misuses of the boundary condition and the way
they affect stellar modeling and stellar evolution. The first one consists in
applying the neutrality condition for convective instability on the
$\textit{radiative}$ side of the convective boundary. The second way of
misusing the boundary condition comes from the process of fixing the convective
boundary through the search for a change of sign of a possibly
\textit{discontinuous} function. We show that these misuses can lead to
completely wrong estimates of convective core sizes with important consequences
for the following evolutionary phases. We point out the advantages of using a
double mesh point at each convective zone boundaries. The specific problem of a
convective shell is discussed and some remarks concerning overshooting are
given.

Solar and Stellar Astrophysics