  We derive a self-consistent local variant of the Thomas-Fermi approximation
for (quasi-)two-dimensional (2D) systems by localizing the Hartree term. The
scheme results in an explicit orbital-free representation of the electron
density and energy in terms of the external potential, the number of electrons,
and the chemical potential determined upon normalization. We test the method
over a variety 2D nanostructures by comparing to the Kohn-Sham 2D-LDA
calculations up to 600 electrons. Accurate results are obtained in view of the
negligible computational cost. We also assess a local upper bound for the
Hartree energy.
