In this paper we study the convergence rate of a finite volume approximation of the compressible Navier--Stokes--Fourier system. To this end we first show the local existence of a highly regular unique strong solution and analyse its global extension in time as far as the density and temperature remain bounded. We make a physically reasonable assumption that the numerical density and temperature are uniformly bounded from above and below. The relative energy provides us an elegant way to derive a priori error estimates between finite volume solutions and the strong solution.
@article{arxiv.2210.15561,
title = {Error estimates of a finite volume method for the compressible Navier--Stokes--Fourier system},
author = {Danica Basaric and Maria Lukacova-Medvidova and Hana Mizerova and Bangwei She and Yuhuan Yuan},
journal= {arXiv preprint arXiv:2210.15561},
year = {2022}
}