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.

翻译：我们为具有可变密度的不压缩纳维埃-斯托克斯方程式提出了一个线性半隐含和分解的限定元素方法。 我们的方法是完全分离的, 并显示为无条件稳定。 速度方程式通过H1等同的限定元素方法解析, 密度方程式则采用带有后处理速度的上风不连续加列金限定元素方法。 事实证明, 所拟议的方法在三维共振聚合体域内, 相近的相当平稳的解决方案中, 相近一致。