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

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Original languageEnglish
Article number2
Journal / PublicationJournal of Scientific Computing
Issue number1
Online published28 Feb 2022
Publication statusPublished - Apr 2022


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.

Research Area(s)

  • Navier-Stokes equations, Variable density, Transport equation, Discontinuous Galerkin methods, PROJECTION METHOD