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arXiv · 2007.13292

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

Buyang Li·Weifeng Qiu·ZongZe Yang
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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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Buyang Li, Weifeng Qiu, ZongZe Yang. 2020-07-27. A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density. https://arxiv.org/abs/2007.13292

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