A Convergent Post-processed Discontinuous Galerkin Method for Incompressible Flow with Variable Density

摘要

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 H-1-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.

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