  The convective overshoot mixing plays an important role in stellar structure
and evolution. However, the overshoot mixing is a long standing problem. The
uncertainty of the overshoot mixing is one of the most uncertain factors in
stellar physics. As it is well known, the convective and overshoot mixing is
determined by the radial chemical component flux. In this paper, a local model
of the radial chemical component flux is established based on the hydrodynamic
equations and some model assumptions. The model is tested in stellar models.
The main conclusions are as follows. (i) The local model shows that the
convective and overshoot mixing could be regarded as a diffusion process, and
the diffusion coefficient for different chemical element is the same. However,
if the non-local terms, i.e., the turbulent convective transport of radial
chemical component flux, are taken into account, the diffusion coefficient for
each chemical element should be in general different. (ii) The diffusion
coefficient of convective / overshoot mixing shows different behaviors in
convection zone and in overshoot region because the characteristic length scale
of the mixing is large in the convection zone and small in the overshoot
region. The overshoot mixing should be regarded as a weak mixing process. (iii)
The result of the diffusion coefficient of mixing is tested in stellar models.
It is found that a single choice of our central mixing parameter leads to
consistent results for a solar convective envelope model as well as for core
convection models of stars with mass from 2M to 10M.
