  In the literature about field emission, finite elements and finite
differences techniques are being increasingly employed to understand the local
field enhancement factor (FEF) via numerical simulations. In theoretical
analyses, it is usual to consider the emitter as isolated, i.e, a single tip
field emitter infinitely far from any physical boundary, except the substrate.
However, simulation domains must be finite and the simulation boundaries
influences the electrostatic potential distribution. In either finite elements
or finite differences techniques, there is a systematic error ($\epsilon$) in
the FEF caused by the finite size of the simulation domain. It is attempting to
oversize the domain to avoid any influence from the boundaries, however, the
computation might become memory and time consuming, especially in full three
dimensional analyses. In this work, we provide the minimum width and height of
the simulation domain necessary to evaluate the FEF with $\epsilon$ at the
desired tolerance. The minimum width ($A$) and height ($B$) are given relative
to the height of the emitter ($h$), that is, $(A/h)_{min} \times (B/h)_{min}$
necessary to simulate isolated emitters on a substrate. We also provide the
$(B/h)_{min}$ to simulate arrays and the $(A/h)_{min}$ to simulate an emitter
between an anode-cathode planar capacitor. At last, we present the formulae to
obtain the minimal domain size to simulate clusters of emitters with precision
$\epsilon_{tol}$. Our formulae account for ellipsoidal emitters and hemisphere
on cylindrical posts. In the latter case, where an analytical solution is not
known at present, our results are expected to produce an unprecedented
numerical accuracy in the corresponding local FEF.
