  Dirac-like Hamiltonians, linear in momentum $k$, describe the low-energy
physics of a large set of novel materials, including graphene, topological
insulators, and Weyl fermions. We show here that the inclusion of a minimal
$k^2$ Wilson's mass correction improves the models and allows for systematic
derivations of appropriate boundary conditions for the envelope functions on
finite systems. Considering only Wilson's masses allowed by symmetry, we show
that the $k^2$ corrections are equivalent to Berry-Mondragon's discontinuous
boundary conditions. This allows for simple numerical implementations of
regularized Dirac models on a lattice, while properly accounting for the
desired boundary condition. We apply our results on graphene nanoribbons
(zigzag and armchair), and on a PbSe monolayer (topological crystalline
insulator). For graphene, we find generalized Brey-Fertig boundary conditions,
which correctly describe the small gap seen on \textit{ab initio} data for the
metallic armchair nanoribbon. On PbSe, we show how our approach can be used to
find spin-orbital-coupled boundary conditions. Overall, our discussions are set
on a generic model that can be easily generalized for any Dirac-like
Hamiltonian.
