  We present a self-consistent Schroedinger-Poisson scheme for simulation of
electrostatic quantum dots defined in gated two-dimensional electron gas formed
at n-AlGaAs/GaAs heterojunction. The computational method is applied to a
quantitative description of transport properties studied experimentally by
Elzermann et al. [Appl. Phys. Lett. {\bf 84}, 4617 (2004)]. The
three-dimensional model describes the electrostatics of the entire device with
a quantum dot that changes shape and floats inside a gated region when the
applied voltages are varied. Our approach accounts for the metal electrodes of
arbitrary geometry and configuration, includes magnetic field applied
perpendicular to the growth direction, electron-electron correlation in the
confined electron system and its interaction with the electron reservoir
surrounding the quantum dot. We calculate the electric field, the space charge
distribution as well as energies and wave functions of confined electrons to
describe opening of two transport channels between the reservoir and the
confined charge puddle. We determine the voltages for charging the dot with up
to 4 electrons.
  The results are in a qualitative and quantitative agreement with the
experimental data.
