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

2020/07/27 by Li, Buyang, Qiu, Weifeng, Yang, ZongZe · 4 citations
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2007.13292

Abstract

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.

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