Error estimates for a numerical method for the compressible Navier-Stokes system on sufficiently smooth domains

TL;DR

This paper derives an unconditional a priori error estimate for a finite volume/finite element numerical method solving the barotropic Navier-Stokes equations on smooth domains, ensuring accuracy without solution bounds.

Contribution

It provides the first error estimate for this numerical method applied to smooth domains without requiring bounds on the numerical solution.

Findings

Error estimate is unconditional and holds without bounds on the numerical solution.

The estimate applies to finite volume/finite element discretizations of the Navier-Stokes system.

The method is validated on polyhedral domains approximating smooth bounded regions.

Abstract

We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier--Stokes equations. The numerical solution on a convenient polyhedral domain approximating a sufficiently smooth bounded domain is compared with an exact solution of the barotropic Navier--Stokes equations with a bounded density. The result is unconditional in the sense that there are no assumed bounds on the numerical solution.