  We propose a linearized semi-implicit and decoupled finite element method for
the incompressible Navier--Stokes equations with variable density. Our method
is fully discrete and shown to be unconditionally stable. The velocity equation
is solved by an H1-conforming finite element method, and an upwind
discontinuous Galerkin finite element method with post-processed velocity is
adopted for the density equation. The proposed method is proved to be
convergent in approximating reasonably smooth solutions in three-dimensional
convex polyhedral domains.
