Convergent finite element methods for compressible barotropic Stokes systems

TL;DR

This paper introduces finite element methods for compressible barotropic Stokes systems, providing convergence results supported by advanced mathematical tools like higher integrability estimates and renormalized formulations.

Contribution

The paper presents novel finite element methods with proven convergence for compressible barotropic Stokes systems, including new analytical techniques for their validation.

Findings

Convergence of the proposed finite element methods is established.

Higher integrability estimates are developed for the discrete density.

Renormalized formulations are used to analyze the density equation.

Abstract

We propose finite element methods for compressible barotropic Stokes systems. We state convergence results for these methods and outline their proofs. The principal tools of the proofs are higher integrability estimates for the discrete density, equations for the discrete effective viscous flux, and renormalized formulations of the numerical method for the density equation.