A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density
Numerical Analysis
2021-12-28 v2 Numerical Analysis
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.
Cite
@article{arxiv.2007.13292,
title = {A convergent post-processed discontinuous Galerkin method for incompressible flow with variable density},
author = {Buyang Li and Weifeng Qiu and ZongZe Yang},
journal= {arXiv preprint arXiv:2007.13292},
year = {2021}
}