  We study $N$ interacting massless Dirac fermions confined in a
two-dimensional quantum dot. Physical realizations of this problem include a
graphene monolayer and the surface state of a strong topological insulator. We
consider both a magnetic confinement and an infinite mass confinement. The
ground state energy is computed as a function of the effective interaction
parameter $\alpha$ from the Hartree-Fock approximation and, alternatively, by
employing the M\"uller exchange functional. For N=2, we compare those
approximations to exact diagonalization results. The Hartree-Fock energies are
highly accurate for the most relevant interaction range $\alpha\alt 2$, but the
M\"uller functional leads to an unphysical instability when $\alpha\agt 0.756$.
Up to 20 particles were studied using Hartree-Fock calculations. Wigner
molecule formation was observed for strong but realistic interactions,
accompanied by a rich peak structure in the addition energy spectrum.
