A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density

07/27/2020

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by   Buyang Li, et al.

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A linearized semi-implicit unconditionally stable decoupled fully discrete finite element method is proposed for the incompressible Navier–Stokes equations with variable density. 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.